{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Quantum mechanics\n", "\n", "Time-independent Schroedinger equation reads\n", "$$\n", "\\left[-\\frac{\\hbar^2}{2m} \\frac{d^2 }{dx^2} + V(x)\\right] \\psi(x) = E \\psi(x).\n", "$$\n", "Let us say we have boundary conditions $\\psi(-L/2) = \\psi(L/2) = 0$.\n", "\n", "In the case of (an)harmonic oscillator we learned how to use the shooting method to find the eigenenergies by combining a root finder (bisection or secant method) with an ODE integrator (such as RK4).\n", "This involved discretizing the space on a grid.\n", "\n", "The problem can also be tackled by linear algebra methods." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Matrix method for eigenenergies and eigenstates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By discretizing the space into $N$ intervals, we can represent the wave function $\\psi(x)$ as an $(N+1)$-dimensional vector $\\mathbf{\\psi} = (\\psi_0,\\ldots,\\psi_{N})$ such that\n", "\n", "$$\n", "\\psi_k = \\psi(x_k), \\qquad x_k = -L/2 + k dx, \\qquad dx = L/N.\n", "$$\n", "\n", "Due to boundary conditions we have $\\psi_0 = \\psi_{N} = 0$, thus effectively we deal with $(N-1)$-dimensional space.\n", "\n", "Each operator becomes a $(N-1)$x$(N-1)$ matrix. By discretizing $\\frac{d^2 }{dx^2}$ by the central difference we get\n", "\n", "$$\n", "\\frac{d^2}{dx^2} \\psi_n \\approx \\frac{\\psi_{n+1} - 2\\psi_n + \\psi_{n-1}}{dx^2}.\n", "$$\n", "\n", "There, the Hamiltonian, has the following matrix representation\n", "\n", "$$\n", "H_{nm} = -\\frac{\\hbar^2}{2m} \\left[ \\delta_{m,n+1} \\psi_{n+1} - 2 \\delta_{m,n} \\psi_{n} + \\delta_{m,n-1} \\psi_{n-1} \\right] + \\delta_{m,n} V(x_n),\n", "$$\n", "\n", "i.e. $H$ is a tridiagonal symmetric matrix.\n", "\n", "Therefore finding the energies and wave function of the system corresponds to the matrix eigenvalue problem for the matrix $H$, i.e. we look for eigenstate $\\psi$ and eigenenergies $E$ such that\n", "$$\n", "\\sum_{m=1}^{N-1} H_{nm} \\psi_m = E \\psi_n\n", "$$\n", "\n", "Let us apply the method to (an)harmonic oscillator we had before." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Constants\n", "me = 9.1094e-31 # Mass of electron\n", "hbar = 1.0546e-34 # Planck's constant over 2*pi\n", "e = 1.6022e-19 # Electron charge\n", "V0 = 50*e\n", "a = 1e-11\n", "N = 100\n", "L = 20*a\n", "dx = L/N\n", "\n", "# Potential functions\n", "def Vharm(x):\n", " return V0 * x**2 / a**2\n", "\n", "def Vanharm(x):\n", " return V0 * x**4 / a**4\n", "\n", "# Construct the Hamiltonian matrix\n", "def HamiltonianMatrix(V):\n", " H = (-hbar**2 / (2*me*dx**2)) * (np.diag((N-2)*[1],-1) + np.diag((N-1)*[-2],0) + np.diag((N-2)*[1],1)) \n", " H += np.diag([V(-0.5 * L + dx*(k+0.5)) for k in range(1,N)],0)\n", " return H\n", "\n", "# Compute the normalisation factor with trapezoidal rule\n", "def integral_psi2(psi, dx):\n", " N = len(psi) - 1\n", " ret = 0\n", " \n", " for k in range(N):\n", " ret += psi[k] * np.conj(psi[k]) + psi[k+1] * np.conj(psi[k+1])\n", " \n", " ret *= 0.5 * dx\n", " \n", " return ret\n", "\n", "# Compute the integral (to determine the sign)\n", "def integral_psi(psi, dx):\n", " N = len(psi) - 1\n", " ret = 0\n", " \n", " for k in range(N//2):\n", " ret += psi[k] + psi[k+1]\n", " \n", " ret *= 0.5 * dx\n", " \n", " return ret" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since our matrix is real symmetric, we can use a straightforward implementation of the QR algorithm.\n", "We thus expect to obtain representation of $H$ in form\n", "$$\n", "H = Q^T A Q\n", "$$\n", "where $A$ is diagonal and contains the energies, while $Q$ is orthogonal and has eigenvectors (wave functions) in its columns." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# Simple implementation of the QR algorithm\n", "# For real symmetric matrix we expect\n", "# A to converge to diagonal matrix with eigenvalues\n", "# and Q to have eigenvectors in each column\n", "def eigen_qr_simple(A, iterations=100):\n", " Ak = np.copy(A)\n", " n = len(A[0])\n", " QQ = np.eye(n)\n", " for k in range(iterations):\n", " Q, R = np.linalg.qr(Ak)\n", " Ak = np.dot(R,Q)\n", " QQ = np.dot(QQ,Q)\n", " return Ak, QQ\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Using simple QR decomposition\n", "First 10 eigenenergies of Harmonic oscillator are\n", "E_ 0 = 137.89885851581894 eV\n", "E_ 1 = 413.4458926008829 eV\n", "E_ 2 = 688.4908722178074 eV\n", "E_ 3 = 963.032414764268 eV\n", "E_ 4 = 1237.0692864045639 eV\n", "E_ 5 = 1510.6049379379701 eV\n", "E_ 6 = 1783.6846685028052 eV\n", "E_ 7 = 2056.5146074219624 eV\n", "E_ 8 = 2329.6277224764217 eV\n", "E_ 9 = 2603.942760131254 eV\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 8.9 s, sys: 1.04 s, total: 9.94 s\n", "Wall time: 1.11 s\n" ] } ], "source": [ "%%time\n", "\n", "print(\"Using simple QR decomposition\")\n", "# Harmonic oscillator\n", "Vpot = Vharm\n", "Vlabel = \"Harmonic oscillator\"\n", "A, Q = eigen_qr_simple(HamiltonianMatrix(Vpot),50)\n", "indices = np.argsort(np.diag(A))\n", "eigenvalues = np.diag(A)[indices]\n", "eigenvectors = [Q[:,indices[i]] for i in range(len(indices))]\n", "Nprint = 10\n", "print(\"First\",Nprint,\"eigenenergies of\", Vlabel, \"are\")\n", "for n in range(Nprint):\n", " print(\"E_\",n,\"=\",eigenvalues[n]/e,\"eV\")\n", "\n", "Nplot = 3\n", "colors = ['r','g','b']\n", "xpoints = [(-0.5 * L + dx*(k+0.5))*1.e10 for k in range(1,N)]\n", "plt.title(Vlabel)\n", "plt.xlabel(\"${x~[\\\\AA]}$\")\n", "plt.ylabel(\"${\\psi(x)~[\\\\AA^{-1/2}]}$\")\n", "for i in range(Nplot):\n", " norm = integral_psi2(eigenvectors[i], dx)\n", " sign = 1\n", " if (integral_psi(eigenvectors[i], dx) < 0.):\n", " sign = -1\n", " # Plot the wave-function\n", " plt.plot(xpoints,1.e-5*sign*eigenvectors[i]/np.sqrt(norm),label='E = ' + \"{:.3f}\".format(eigenvalues[i]/e) + ' eV',color=colors[i])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "First 10 eigenenergies of Anharmonic oscillator are\n", "E_ 0 = 204.8415643532322 eV\n", "E_ 1 = 732.3479746488032 eV\n", "E_ 2 = 1432.2531583599684 eV\n", "E_ 3 = 2228.057822724745 eV\n", "E_ 4 = 3097.5257850925673 eV\n", "E_ 5 = 4025.6461383175433 eV\n", "E_ 6 = 5001.906288357331 eV\n", "E_ 7 = 6018.30839402047 eV\n", "E_ 8 = 7068.619615567106 eV\n", "E_ 9 = 8148.325531154665 eV\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 8.54 s, sys: 1.19 s, total: 9.73 s\n", "Wall time: 1.04 s\n" ] } ], "source": [ "%%time\n", "# Anharmonic oscillator\n", "Vpot = Vanharm\n", "Vlabel = \"Anharmonic oscillator\"\n", "A, Q = eigen_qr_simple(HamiltonianMatrix(Vpot),50)\n", "indices = np.argsort(np.diag(A))\n", "eigenvalues = np.diag(A)[indices]\n", "eigenvectors = [Q[:,indices[i]] for i in range(len(indices))]\n", "Nprint = 10\n", "print(\"First\",Nprint,\"eigenenergies of\", Vlabel, \"are\")\n", "for n in range(Nprint):\n", " print(\"E_\",n,\"=\",eigenvalues[n]/e,\"eV\")\n", " \n", "Nplot = 3\n", "colors = ['r','g','b']\n", "xpoints = [(-0.5 * L + dx*(k+0.5))*1.e10 for k in range(1,N)]\n", "plt.title(Vlabel)\n", "plt.xlabel(\"${x~[\\\\AA]}$\")\n", "plt.ylabel(\"${\\psi(x)~[\\\\AA^{-1/2}]}$\")\n", "for i in range(Nplot):\n", " norm = integral_psi2(eigenvectors[i], dx)\n", " sign = 1\n", " if (integral_psi(eigenvectors[i], dx) < 0.):\n", " sign = -1\n", " # Plot the wave-function\n", " plt.title(Vlabel)\n", " plt.plot(xpoints,1.e-5*sign*eigenvectors[i]/np.sqrt(norm),label='E = ' + \"{:.3f}\".format(eigenvalues[i]/e) + ' eV',color=colors[i])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also use efficient implementations of the eigenvalues/eigenvectors computation in numpy." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "First 9 eigenenergies of Harmonic oscillator are\n", "E_ 0 = 137.89885851582747 eV\n", "E_ 1 = 413.4458926008785 eV\n", "E_ 2 = 688.4908722176755 eV\n", "E_ 3 = 963.0324138966929 eV\n", "E_ 4 = 1237.0691216855612 eV\n", "E_ 5 = 1510.5995897804717 eV\n", "E_ 6 = 1783.622425735222 eV\n", "E_ 7 = 2056.1364082137375 eV\n", "E_ 8 = 2328.1413677481114 eV\n", "CPU times: user 1.4 s, sys: 482 ms, total: 1.88 s\n", "Wall time: 211 ms\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%time\n", "Vpot = Vharm\n", "Vlabel = \"Harmonic oscillator\"\n", "eigenvalues, eigenvectors = np.linalg.eigh(HamiltonianMatrix(Vpot))\n", "Nprint = 9\n", "print(\"First\",Nprint,\"eigenenergies of\", Vlabel, \"are\")\n", "for n in range(Nprint):\n", " print(\"E_\",n,\"=\",eigenvalues[n]/e,\"eV\")\n", " \n", "Nplot = 3\n", "colors = ['r','g','b']\n", "xpoints = [(-0.5 * L + dx*(k+0.5))*1.e10 for k in range(1,N)]\n", "plt.title(Vlabel)\n", "plt.xlabel(\"${x~[\\\\AA]}$\")\n", "plt.ylabel(\"${\\psi(x)~[\\\\AA^{-1/2}]}$\")\n", "for i in range(Nplot):\n", " norm = integral_psi2(eigenvectors[:,i], dx)\n", " sign = 1\n", " if (integral_psi(eigenvectors[:,i],dx) < 0.):\n", " sign = -1\n", " # Plot the wave-function\n", " plt.plot(xpoints,1e-5*sign*eigenvectors[:,i]/np.sqrt(norm),label='E = ' + \"{:.3f}\".format(eigenvalues[i]/e) + ' eV',color=colors[i])" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "First 9 eigenenergies of Anharmonic oscillator are\n", "E_ 0 = 204.841564353175 eV\n", "E_ 1 = 732.3479746488514 eV\n", "E_ 2 = 1432.253158359968 eV\n", "E_ 3 = 2228.0578227239957 eV\n", "E_ 4 = 3097.525784098384 eV\n", "E_ 5 = 4025.6460160184683 eV\n", "E_ 6 = 5001.902410892116 eV\n", "E_ 7 = 6018.256522464476 eV\n", "E_ 8 = 7068.232404050683 eV\n", "CPU times: user 760 ms, sys: 377 ms, total: 1.14 s\n", "Wall time: 124 ms\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%time\n", "Vpot = Vanharm\n", "Vlabel = \"Anharmonic oscillator\"\n", "eigenvalues, eigenvectors = np.linalg.eigh(HamiltonianMatrix(Vpot))\n", "Nprint = 9\n", "print(\"First\",Nprint,\"eigenenergies of\", Vlabel, \"are\")\n", "for n in range(Nprint):\n", " print(\"E_\",n,\"=\",eigenvalues[n]/e,\"eV\")\n", " \n", "Nplot = 3\n", "colors = ['r','g','b']\n", "xpoints = [(-0.5 * L + dx*(k+0.5))*1.e10 for k in range(1,N)]\n", "plt.title(Vlabel)\n", "plt.xlabel(\"${x~[\\\\AA]}$\")\n", "plt.ylabel(\"${\\psi(x)~[\\\\AA^{-1/2}]}$\")\n", "for i in range(Nplot):\n", " norm = integral_psi2(eigenvectors[:,i], dx)\n", " sign = 1\n", " if (integral_psi(eigenvectors[:,i],dx) < 0.):\n", " sign = -1\n", " # Plot the wave-function\n", " plt.plot(xpoints,1e-5*sign*eigenvectors[:,i]/np.sqrt(norm),label='E = ' + \"{:.3f}\".format(eigenvalues[i]/e) + ' eV',color=colors[i])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Time evolution of free particle wave function\n", "\n", "*Exercise 9.8 from M. Newman, Computational Physics*\n", "\n", "The time-dependent Schroedinger equation reads\n", "\n", "$$\n", "\\hat{H} \\psi = i \\hbar \\frac{\\partial \\psi}{\\partial t}~.\n", "$$\n", "\n", "e.g. for a free particle it reads\n", "\n", "$$\n", "-\\frac{\\hbar^2}{2m} \\frac{\\partial^2 \\psi}{\\partial x^2} = i \\hbar \\frac{\\partial \\psi}{\\partial t}~.\n", "$$\n", "\n", "Formal solution be written as\n", "\n", "$$\n", "\\psi(t) = e^{-\\frac{it}{\\hbar} \\hat{H}} \\psi(0),\n", "$$\n", "\n", "with $\\hat{U}(t) = e^{-\\frac{it}{\\hbar} \\hat{H}}$ being the time evolution operator.\n", "It is a unitary operator $U^\\dagger U = \\hat{I}$, therefore, the norm of the wave function $|\\psi|^2$ is conserved.\n", "\n", "We can study time evolution by succesively applying approximate $\\hat{U}(\\Delta t)$ over small time intervals.\n", "\n", "- FTCS scheme\n", "$$\n", "\\hat{U}(\\Delta t) = e^{-\\frac{i \\Delta t}{\\hbar} \\hat{H}} \\approx 1 - \\frac{i \\Delta t}{\\hbar} \\hat{H}\n", "$$\n", "Such an operator is not unitary since\n", "$$\n", "U^\\dagger (\\Delta t) = 1 + \\frac{i \\Delta t}{\\hbar} \\hat{H} \\neq \\hat{U}(\\Delta t).\n", "$$\n", "If $U$ is applied to an energy eigenstate $\\psi_l$, such that $\\hat{H} \\psi_l = E_k \\psi_l$, we get\n", "$$\n", "\\psi_l(N \\Delta t) = \\lambda_l^N \\psi_l(0),\n", "$$\n", "where $\\lambda_l = \\left[1 - \\frac{i \\Delta t E_l}{\\hbar} \\right]$.\n", "Since $|\\lambda_l| > 1$, the method is unstable.\n", "\n", "- Implicit scheme\n", "\n", "We apply the approximation of the FTCS scheme to the inverse of $\\hat{U}(\\Delta t)$.\n", "This implies\n", "$$\n", "\\hat{U}(\\Delta t) = e^{-\\frac{i \\Delta t}{\\hbar} \\hat{H}} \\approx \\frac{1}{1 + \\frac{i \\Delta t}{\\hbar} \\hat{H}}.\n", "$$\n", "The operator is also non-unitary. The method is stable because\n", "$$\n", "|\\lambda_l| = \\left| \\frac{1}{1 + \\frac{i \\Delta t}{\\hbar} E_L} \\right| < 1,\n", "$$\n", "but the method does not conserve the norm of the wave function.\n", "\n", "- Crank-Nicholson scheme\n", "\n", "Crank-Nicholson scheme takes the combitation of FTCS and implicit schemes.\n", "This correspons to a rational approximation of $\\hat{U}(\\Delta t)$:\n", "$$\n", "\\hat{U}(\\Delta t) = e^{-\\frac{i \\Delta t}{\\hbar} \\hat{H}} \\approx \\frac{1 - \\frac{i \\Delta t}{\\hbar} \\hat{H}}{1 + \\frac{i \\Delta t}{\\hbar} \\hat{H}}.\n", "$$\n", "\n", "This operator is unitary (for an hermitian $\\hat{H}$), $U^\\dagger U = U U^\\dagger$, and conserves the norm of the wave function." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us consider the particle in a box of length $L$.\n", "We thus have boundary conditions $\\psi(0) = \\psi(L) = 0$.\n", "\n", "Given some initial wave function $\\psi(x)$, we can numerically integrate the Schroedinger equation to study the time evolution of the wave function.\n", "\n", "Let us write the equation in a form:\n", "$$\n", "\\frac{\\partial \\psi}{\\partial t} = \\frac{i \\hbar}{2m} \\frac{\\partial^2 \\psi}{\\partial x^2}.\n", "$$\n", "We can now use the central difference approximation for $\\partial^2 \\psi / \\partial x^2$:\n", "$$\n", "\\frac{\\partial \\psi}{\\partial t} \\approx \\frac{i \\hbar}{2ma^2} \\left[ \\psi(x+a,t) - 2 \\psi(x,t) + \\psi(x-a,t) \\right].\n", "$$\n", "\n", "This gives us discretized wave function in coordinate space, in full analogy to the heat equation that we studied before. The only difference is that now we are dealing with complex-valued functions.\n", "\n", "We now need to apply the prescription for time evolution.\n", "The options are:\n", "- FTCS scheme\n", "$$\n", "\\psi(x,t+h) = \\psi(x,t) + h \\frac{i \\hbar}{2ma^2} \\left[ \\psi(x+a,t) - 2 \\psi(x,t) + \\psi(x-a,t) \\right],\n", "$$\n", "or\n", "$$\n", "\\psi^{n+1}_k = \\psi^n_k + h \\frac{i \\hbar}{2ma^2} (\\psi^n_{k+1} - 2 \\psi^n_k + \\psi^n_{k-1}).\n", "$$\n", "- Implicit scheme\n", "$$\n", "\\psi^{n+1}_k = \\psi^n_k + h \\frac{i \\hbar}{2ma^2} (\\psi^{n+1}_{k+1} - 2 \\psi^{n+1}_k + \\psi^{n+1}_{k-1}).\n", "$$\n", "- Crank-Nicholson scheme\n", "$$\n", "\\psi^{n+1}_k = \\psi^n_k + \\frac{h}{2} \\frac{i \\hbar}{2ma^2} (\\psi^n_{k+1} - 2 \\psi^n_k + \\psi^n_{k-1}) + \\frac{h}{2} \\frac{i \\hbar}{2ma^2} (\\psi^{n+1}_{k+1} - 2 \\psi^{n+1}_k + \\psi^{n+1}_{k-1}).\n", "$$\n", "\n", "To preserve unitarity it makes sense to apply Crank-Nicholson scheme.\n", "In this case we need to solve the tridiagonal system of equations at each time step." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "# Solve tridiagonal system of linear equations\n", "# d: vector of diagonal elements\n", "# l: vector of elements on the lower subdiagonal\n", "# u: vector of elements on the upper superdiagonal\n", "# v0: right-hand-side vector\n", "def linsolve_tridiagonal(d, l, u, v0):\n", " # Initialization\n", " N = len(v0)\n", " a = d.copy() # Current diagonal elements\n", " b = u.copy() # Current upper diagonal elements\n", " v = v0.copy()\n", " \n", " # Gaussian elimination\n", " for r in range(N):\n", " if (a[r] == 0.):\n", " print(\"Diagonal element is zero! Cannot solve the tridiagonal system with simple Gaussian elimination\")\n", " return None\n", " b[r] /= a[r]\n", " v[r] /= a[r]\n", " a[r] = 1.\n", " if (r < N - 1):\n", " a[r + 1] -= l[r+1] * b[r]\n", " v[r + 1] -= l[r+1] * v[r]\n", " \n", " # Backsubstitution\n", " x = np.empty(N,dtype=np.cdouble)\n", " \n", " x[N - 1] = v[N - 1]\n", " for r in range(N-2,-1,-1):\n", " x[r] = v[r] - b[r] * x[r + 1]\n", " \n", " return x" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "me = 9.1094e-31 # Mass of electron in kg\n", "hbar = 1.0546e-34 # Planck's constant over 2*pi\n", "\n", "# Single Crank-Nicholson scheme iteration for the Schroedinger equation\n", "# psi is a complex-valued wave function discretized in space\n", "# r = i * h * hbar / (2*m*a^2)\n", "# scheme: 0 - FTCS, 1 - implicit, 2 - Crank-Nicholson\n", "def schrodinger_finitediff_iteration(psi, r, scheme = 2):\n", " N = len(psi) - 1\n", " \n", " psinew = np.empty_like(psi, dtype=np.cdouble)\n", " \n", " # Boundary conditions\n", " psinew[0] = psi[0]\n", " psinew[N] = psi[N]\n", " \n", " if (scheme == 0):\n", " for i in range(1,N):\n", " psinew[i] = psi[i] + r * (psi[i+1] - 2 * psi[i] + psi[i-1])\n", " elif (scheme == 1):\n", " d = np.full(N-1, 1 + 2*r)\n", " ud = np.full(N-1, -r)\n", " ld = np.full(N-1, -r)\n", "\n", " # Implicit scheme matrix\n", " v = np.array(psi[1:N])\n", " v[0] += r * psi[0]\n", " v[N-2] += r * psi[N]\n", "\n", " # Solve tridiagonal system\n", " psinew[1:N] = linsolve_tridiagonal(d, ld, ud, v)\n", " else:\n", " d = np.full(N-1, 2*(1+r))\n", " ud = np.full(N-1, -r)\n", " ld = np.full(N-1, -r)\n", "\n", " # Crank-Nicolson explicit step\n", " v = psi[1:N]*2*(1-r) + psi[:-2]*r + psi[2:]*r\n", " v[0] += r * psi[0]\n", " v[N-2] += r * psi[N]\n", "\n", " # Solve tridiagonal system\n", " psinew[1:N] = linsolve_tridiagonal(d, ld, ud, v)\n", " \n", " return psinew\n", "\n", "def schrodinger_finitediff_solve(psi0, h, nsteps, a, m = me, scheme = 2):\n", " psi = psi0.copy()\n", " r = 1j * h * hbar / (2 * m * a**2)\n", " for i in range(nsteps):\n", " psi = schrodinger_finitediff_iteration(psi, r, scheme)\n", " \n", " return psi\n" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAk8AAAHHCAYAAACmzLxGAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjAsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvlHJYcgAAAAlwSFlzAAAPYQAAD2EBqD+naQAAuyJJREFUeJzsnXd8FHX6x9+zJb0XAgkl9N47imKhIzYsp2LHdsVynneo6Kl3x533U7HrnSgWDhuKjaqCoKB0kF5DQkggvZct8/tjMpssabuzm4TA8/a1r93MfmfmOwnufPZ5nu/nUVRVVREEQRAEQRA8wtTSExAEQRAEQWhNiHgSBEEQBEHwAhFPgiAIgiAIXiDiSRAEQRAEwQtEPAmCIAiCIHiBiCdBEARBEAQvEPEkCIIgCILgBSKeBEEQBEEQvEDEkyAIgiAIgheIeBKEs5QFCxagKEqdj4cffrilp9fsnDhxgr/+9a9s37691nt//etfURTF62PeeuutJCcn+z65KvS/WUpKit+O6Qv67yU7O7ulpyIIZxSWlp6AIAhNyzvvvEOvXr3ctiUmJrbQbFqOEydO8NRTT5GcnMygQYPc3rvzzjuZNGlSy0ysBlOnTmXDhg20a9eupaciCEIDiHgShLOcfv36MWzYMI/G2mw2FEXBYjl7PhocDgd2u73BMe3bt6d9+/bNNKP6iY+PJz4+vqWnIQhCI0jaThDOUdasWYOiKLz//vv88Y9/JCkpicDAQA4dOgTAt99+yyWXXEJERAQhISGcd955fPfdd7WOc/DgQW644QbatGlDYGAgvXv35tVXX/VoDoqi8Lvf/Y4333yTHj16EBgYSJ8+ffjwww/dxmVlZXHffffRp08fwsLCaNOmDRdffDHr1q1zG5eSkoKiKDz77LP87W9/o3PnzgQGBrJ69WqGDx8OwG233eZKX/71r38F6k/b/e9//2P06NGEhYURFhbGoEGDmD9/foPXpKoqr732GoMGDSI4OJjo6GhmzJjBkSNHGv191JW2GzduHP369WPTpk2MHTuWkJAQunTpwj//+U+cTmejx3z11Ve54IILaNOmDaGhofTv359nn30Wm83W6L46aWlpXHXVVURERBAZGclNN91EVlaW2xin08mzzz5Lr169CAwMpE2bNtx8880cP37cNeaee+4hKCiILVu2uO13ySWXkJCQQEZGhsdzEoSWRMSTIJzl6JGXmo+azJ49m9TUVN544w2++uor2rRpwwcffMCECROIiIjg3Xff5eOPPyYmJoaJEye6Cag9e/YwfPhwdu3axXPPPcfXX3/N1KlT+cMf/sBTTz3l0fy+/PJLXnrpJZ5++mk+/fRTOnXqxG9+8xs+/fRT15jc3FwAnnzySb755hveeecdunTpwrhx41izZk2tY7700kt8//33/N///R/Lli0jMTGRd955B4DHH3+cDRs2sGHDBu6888565/XEE09w4403kpiYyIIFC/j888+55ZZbOHbsWIPXc/fdd/PAAw9w6aWXsmTJEl577TV2797NmDFjOHnypEe/k9PJzMzkxhtv5KabbuLLL79k8uTJzJ49mw8++KDRfQ8fPswNN9zA+++/z9dff80dd9zBv//9b+6++26Pz3/llVfSrVs3Pv30U/7617+yZMkSJk6c6CbA7r33Xv785z8zfvx4vvzyS5555hmWL1/OmDFjXDVT8+bNo3fv3lx77bXk5+cD8NRTT7FmzRo++OADSVcKrQdVEISzknfeeUcF6nzYbDZ19erVKqBecMEFbvuVlJSoMTEx6mWXXea23eFwqAMHDlRHjBjh2jZx4kS1ffv2akFBgdvY3/3ud2pQUJCam5vb4BwBNTg4WM3MzHRts9vtaq9evdRu3brVu5/dbldtNpt6ySWXqFdeeaVr+9GjR1VA7dq1q1pZWem2z6ZNm1RAfeedd2od78knn1RrfhweOXJENZvN6o033tjg/G+55Ra1U6dOrp83bNigAupzzz3nNi4tLU0NDg5WH3nkkQaPp//Njh496tp24YUXqoD6yy+/uI3t06ePOnHixAaPdzoOh0O12Wzqe++9p5rN5kb/Pvrv5cEHH3TbvnDhQhVQP/jgA1VVVXXv3r0qoN53331u43755RcVUB999FHXtoMHD6oRERHqFVdcoX777beqyWRSH3/8ca+uQxBaGok8CcJZznvvvcemTZvcHjVrmq6++mq38evXryc3N5dbbrnFLVrldDqZNGkSmzZtoqSkhPLycr777juuvPJKQkJC3MZOmTKF8vJyfv7550bnp6dsdMxmM9dddx2HDh1yS/m88cYbDBkyhKCgICwWC1arle+++469e/fWOub06dOxWq1Gfl0ArFq1CofDwW9/+1uv9vv6669RFIWbbrrJ7ffRtm1bBg4cWGeUzBPatm3LiBEj3LYNGDCg0SgYwLZt25g+fTqxsbGYzWasVis333wzDoeDAwcOeHT+G2+80e3na6+9FovFwurVqwFcz7feeqvbuBEjRtC7d2+3aGW3bt3473//y5IlS5g2bRpjx451pU8FobVw9lSFCoJQJ717926wYPz0VImeWpoxY0a9++Tm5mIymbDb7bz88su8/PLLdY7zZIl727Zt692Wk5ND+/btef755/njH//IPffcwzPPPENcXBxms5k5c+bUKZ58Tf/o9TzeFpGfPHkSVVXdxGBNunTpYmg+sbGxtbYFBgZSVlbW4H6pqamMHTuWnj178uKLL5KcnExQUBAbN27kt7/9baP765z+N7JYLMTGxpKTkwPgeq7r956YmFhL5E2dOpWEhAROnjzJQw89hNls9mgegnCmIOJJEM5xTi+UjouLA+Dll19m1KhRde6TkJCA3W7HbDYzc+bMeiM0nTt3bvT8mZmZ9W7TRcMHH3zAuHHjeP31193GFRUV1XlMI55NNdFXvB0/fpwOHTp4vF9cXByKorBu3ToCAwNrvV/XtqZkyZIllJSU8Nlnn9GpUyfX9rq8rhoiMzOTpKQk1892u52cnBzX30d/zsjIqCU4T5w44fo3pXPPPfdQVFRE3759+cMf/sDYsWOJjo72ak6C0JKIeBIEwY3zzjuPqKgo9uzZw+9+97t6xwUEBHDRRRexbds2BgwYQEBAgKHzfffdd5w8edIVrXE4HHz00Ud07drVdSNWFKWW8Ni5cycbNmzwWNzo+3sSbZkwYQJms5nXX3+d0aNHe3wt06ZN45///Cfp6elce+21Hu/XVOgisubvTlVV/vvf/3p1nIULFzJ06FDXzx9//DF2u51x48YBcPHFFwOayNVXNQJs2rSJvXv38thjj7m2vfXWW3zwwQe8/fbbXHjhhQwZMoTbbruNJUuWeHt5gtBiiHgSBMGNsLAwXn75ZW655RZyc3OZMWMGbdq0ISsrix07dpCVleWKAL344oucf/75jB07lnvvvZfk5GSKioo4dOgQX331Fd9//32j54uLi+Piiy9mzpw5hIaG8tprr7Fv3z43u4Jp06bxzDPP8OSTT3LhhReyf/9+nn76aTp37tyoh5NO165dCQ4OZuHChfTu3ZuwsDASExPrNAxNTk7m0Ucf5ZlnnqGsrIzf/OY3REZGsmfPHrKzs+tdSXjeeedx1113cdttt7F582YuuOACQkNDycjI4Mcff6R///7ce++9Hs3XH4wfP56AgAB+85vf8Mgjj1BeXs7rr79OXl6eV8f57LPPsFgsjB8/nt27dzNnzhwGDhzoEog9e/bkrrvu4uWXX8ZkMjF58mRSUlKYM2cOHTp04MEHHwTg119/5Q9/+AO33HILt912GwDz589nxowZzJs3jwceeMCv1y8ITUZLV6wLgtA06Cu3Nm3aVOf7+mq7Tz75pM73f/jhB3Xq1KlqTEyMarVa1aSkJHXq1Km1xh89elS9/fbb1aSkJNVqtarx8fHqmDFj1L/97W+NzhFQf/vb36qvvfaa2rVrV9Vqtaq9evVSFy5c6DauoqJCffjhh9WkpCQ1KChIHTJkiLpkyZJaq9301Xb//ve/6zzfokWL1F69eqlWq1UF1CeffFJV1dqr7XTee+89dfjw4WpQUJAaFhamDh482G213unn13n77bfVkSNHqqGhoWpwcLDatWtX9eabb1Y3b97c4O+jvtV2ffv2rTW2vnOfzldffaUOHDhQDQoKUpOSktQ//elP6rJly1RAXb16dYP76r+XLVu2qJdddpkaFhamhoeHq7/5zW/UkydPuo11OBzqv/71L7VHjx6q1WpV4+Li1JtuuklNS0tTVVVVi4uL1V69eql9+vRRS0pK3Pb97W9/q1qt1lorCgXhTEVRVVVtMeUmCMI5jaIo/Pa3v+WVV15p6akIgiB4jFgVCIIgCIIgeIGIJ0EQBEEQBC+QgnFBEFoMqRoQBKE1IpEnQRAEQRAELxDxJAiCIAiC4AUingRBEARBELxAap6aAKfTyYkTJwgPD/e5TYQgCIIgCM2DqqoUFRWRmJiIyVR/fEnEUxNw4sQJr/phCYIgCIJw5pCWltZgY3ART01AeHg4oP3yIyIiWng2giAIgiB4QmFhIR06dHDdx+tDxFMToKfqIiIiRDwJgiAIQiujsZIbKRgXBEEQBEHwAhFPgiAIgiAIXiDiSRAEQRAEwQuk5kkQBEEQ/ITD4cBms7X0NIR6sFqtmM1mn48j4kkQBEEQfERVVTIzM8nPz2/pqQiNEBUVRdu2bX3yYRTxJAiCIAg+ogunNm3aEBISIgbJZyCqqlJaWsqpU6cAaNeuneFjiXgSBEEQBB9wOBwu4RQbG9vS0xEaIDg4GIBTp07Rpk0bwyk8KRgXBEEQBB/Qa5xCQkJaeCaCJ+h/J19q00Q8CYIgCIIfkFRd68AffycRT4IgCIIgCF7QqsXT2rVrueyyy0hMTERRFJYsWdLoPj/88ANDhw4lKCiILl268MYbb9Qas3jxYvr06UNgYCB9+vTh888/b4LZC4IgCILQGmnV4qmkpISBAwfyyiuveDT+6NGjTJkyhbFjx7Jt2zYeffRR/vCHP7B48WLXmA0bNnDdddcxc+ZMduzYwcyZM7n22mv55ZdfmuoyBEEQBEFoRSiqqqotPQl/oCgKn3/+OVdccUW9Y/785z/z5ZdfsnfvXte2e+65hx07drBhwwYArrvuOgoLC1m2bJlrzKRJk4iOjmbRokUezaWwsJDIyEgKCgqkMbAgnEWU28vZmLmRYEswQ9oMwWzy3WxPaP2Ul5dz9OhROnfuTFBQUEtP56whJyeH3r17s3HjRpKTkxsdP2PGDMaMGcNDDz3U4LiG/l6e3r9bdeTJWzZs2MCECRPctk2cOJHNmze7qu7rG7N+/fp6j1tRUUFhYaHbQxCEs4NKRyVr0tbwl3V/4cKPLuS33/2W21fczqWfXso/fvkH205tw6k6W3qagmCIW2+9FUVRUBQFi8VCx44duffee8nLy2vpqTF37lwuu+wyj4QTwBNPPMHf//73ZrkHn1PiKTMzk4SEBLdtCQkJ2O12srOzGxyTmZlZ73Hnzp1LZGSk69GhQwf/T14QhGbF5rTx7KZnGffxOH7//e/55sg3lNpLaRvaloiACLLLslm0bxE3L7uZCZ9OYOHehS09ZUEwxKRJk8jIyCAlJYW33nqLr776ivvuu69F51RWVsb8+fO58847Pd5nwIABJCcns3Bh0/+/eE6JJ6i9RFHPWtbcXteYhpY2zp49m4KCAtcjLS3NjzMWBKG5sTltPPLDI7y/532KKouID47npt438f7k91l59UrWXLuGVy95lcu6XEaoNZSTpSf558Z/8vr211t66sIZgKqqlFbaW+RhpBInMDCQtm3b0r59eyZMmMB1113HypUr3a7n2WefpUuXLgQHBzNw4EA+/fTTBo+5ZMkSIiIiUFWVQ4cOoSgK6enpOJ1OQkNDWb58eYP7L1u2DIvFwujRo13bFi1aRFBQEOnp6a5td955JwMGDKCgoACA6dOne1xi4wvnlMN427Zta0WQTp06hcVicbnC1jfm9GhUTQIDAwkMDPT/hAVBaHZsTht/Xvtnvk39FqvJyj/G/oPxHce71TdZzVYuaH8BF7S/gApHBe/ufpeXt73MazteQ1EU7hl4TwtegdDSlNkc9HliRYuce8/TEwkJMH5rP3LkCMuXL8dqtbq2Pf7443z22We8/vrrdO/enbVr13LTTTcRHx/PhRdeWOdxtm/fzsCBA1EUhZ07dxIbG0tSUhL79u2jtLSUgQMHNjiPtWvXMmzYMLdt119/Pf/85z+ZO3cur7zyCk899RQrVqzg559/JjIyEoARI0Ywd+5cKioqmvS+fE6Jp9GjR/PVV1+5bVu5ciXDhg1z/UMZPXo0q1at4sEHH3QbM2bMmGadqyAIzY8unFYdW4XVZGXeRfO4oP0FDe4TaA7krgF3YTFZeGHLC7y6/VUUFO4eeHczzVoQfOPrr78mLCwMh8NBeXk5AM8//zygrWp//vnn+f77711RoC5duvDjjz/y5ptv1iueduzYwaBBg+p8HR8fT7t27fj666/54x//iNPp5M9//rNbii4lJYXExES3YyqKwt///ndmzJhBYmIiL774IuvWrSMpKck1JikpiYqKCjIzM+nUqZNffj910arFU3FxMYcOHXL9fPToUbZv305MTAwdO3Zk9uzZpKen89577wHayrpXXnmFhx56iFmzZrFhwwbmz5/vFuK7//77ueCCC/jXv/7F5ZdfzhdffMG3337Ljz/+2OzXJwhC82F32pm9bjarjq3ShNC4FxoVTjW5vd/tqKrKvK3zeGX7K5gUE7MGzGrCGQtnKsFWM3uenthi5/aWiy66iNdff53S0lLeeustDhw4wO9//3sA9uzZQ3l5OePHj3fbp7KyksGDB9d7zO3btzNt2jRAE0x6pEmPSNntdh566CFWr15NREQEQ4YM4aqrriImJgbQap7qWrk4bdo0+vTpw1NPPcXKlSvp27ev+/VX9a4rLS31+vfgDa1aPG3evJmLLrrI9bO+PPGWW25hwYIFZGRkkJqa6nq/c+fOLF26lAcffJBXX32VxMREXnrpJa6++mrXmDFjxvDhhx/y+OOPM2fOHLp27cpHH33EyJEjm+/CBEFoVlRV5bEfH2NFygosJgvzxs3jwg51f6NuiDv634GKyotbX+SlbS8RYA7glr63NMGMhTMZRVF8Sp01N6GhoXTr1g2Al156iYsuuoinnnqKZ555BqdTW0n6zTffuEV4gHrTYkVFRaSkpNC/f39AE0/6fXbr1q0MGjSIjRs30rdvX9cxp0yZwooVK/jNb34DQFxcXJ0r/lasWMG+fftwOBx1ltPk5uYCEB8f7/XvwRtaz1+3DsaNG9dgcdyCBQtqbbvwwgvZunVrg8edMWMGM2bM8HV6giC0Er45+g1Ljy51RZyMCCedO/vfiaqqvLTtJeZtmcfoxNH0iO7hx9kKQtPy5JNPMnnyZO69915Xt43U1NR6U3Snk5GRAUB4eDgFBQWkpKQwaNAgsrKy+OGHH/jjH//IiRMn3MRY+/bt3QrBBw8ezAcffOB23K1bt3LNNdfw5ptv8uGHHzJnzhw++eQTtzG7du2iffv2xMXFGb18jzjnVtsJgiDUpKCigH9v+jcA9w68l3Edxvl8zFkDZnFJx0uwq3ae3vC0+EAJrYpx48bRt29f/vGPfxAeHs7DDz/Mgw8+yLvvvsvhw4fZtm0br776Ku+++26d+yclJRESEsLzzz/PmjVrsFqtlJeXc9VVVzFixAjGjx9fZ+Cj5qr2iRMnsnv3blf0KSUlhalTp/KXv/yFmTNn8vTTT7N48WK2bNnidox169bV8mpsCkQ8CYJwTjNv6zxyy3PpEtmF2/re5rfj/mXEXwixhLAjaweLDy6mqNzGx5vSOHCyyG/nEISm4qGHHuK///0vaWlpPPPMMzzxxBPMnTuX3r17M3HiRL766is6d+5c576hoaF88sknfP/991xxxRXYbDYmT57MqFGj+Oabb1AUhaSkJLdI0/Hjx2nXrp3r5/79+zNs2DA+/vhjcnNzmTx5MtOnT+fRRx8FYOjQoVx22WU89thjrn3Ky8v5/PPPmTWr6WsNz5r2LGcS0p5FEFoH209tZ+aymQC8M/EdhrUd1sge3vH+nvd5dtOzBCihVKY8TFFpMP2TIvnq9+f79TxCyyLtWernhhtuAGDhwoVukSW73U7v3r1Zs2aNq2D8559/dtkGASxdupSHH36YXbt2YTI1Hut59dVX+eKLL9w8qurCH+1ZWnXNkyAIglFsThtPbXgKgCu6XeF34ZSWW8r+AwNwlidSGXQCW9QXUHo9h04VN2q8KwhnC/v37+emm26q9e/dYrHw3HPPcdFFF+F0OnnkkUfchBNoReQHDx4kPT3do84dVquVl19+2a/zrw8RT4IgnJO8v+d9DuUfIiowioeGNtxI1FsyCsoY/8IPlNucmIKuJDT5NayR27EXDKWspDvZxZXEh4uxrnB2Y7fb2b17NwMGDKjz/enTpzN9+vQGj3H//fd7fL677rrLq/n5gtQ8CYJwzpFenO5qpfLQ0IeIDor26/H3nCik3OakTXggH9w0g9/0uh6AkMQvQbGRmtu0HjSCcCZgsVgoLy/nkksuaemp+B0RT4IgnHPM/WUu5Y5yhiYM5YpuV/j9+CcKNJfmgR2iGNMtjt8P+T3xwfGoliwCYtdwPE/EkyC0ZkQ8CYJwTrEjawc/HP8Bi2LhiVFPNEnt0Yn8MgASI7Vi1PCAcB4Z8QgAAbHrOJB10u/nFASh+RDxJAjCOcX8X+cDMK3rNLpEdWmSc2RUiad2UcGubRM7TSTWmoxiqmR91pdNcl5BEJoHEU+CIJwzHM4/zOq01Sgo3NbPf55Op6On7dpFVi+DVhSFS9pptU9HK5dTapPUnSC0VkQ8CYJwzvD2rrcBuKTjJXSJbJqoE2ir7QCSakSeACZ1noCzMhaHUsJnBz9rsvMLgtC0iHgSBOGc4ETxCZYeWQpoDXybCqdTJVOPPJ0mnjrHRVCZcwEAC3a/i81ha7J5CILQdIh4EgThnODd3e9iV+2MbDeSfnH9muw82cUV2BwqJgUSTvNyig0NwFo2HKc9nJOlmXxz9Jsmm4cgCE2HiCdBEM56cstzXWmyO/vf2aTn0uud2oQHYTG7f8QqikLH6EhsOVp7lrd3vS1NgwWhFSLiSRCEs56FexdS7iinb2xfRrYd2aTn0lfaJUbV3eOsfXQIlfkjCTSFcrTgKKtTVzfpfARB8D8ingRBOKsprixm0b5FgBZ1auqecifqqXfS6RgTAs4gugZNAGD+rvlIf3ZBaF2IeBIE4azmkwOfUFRZRHJEMhd3vLjJz3e6QebpdIzRRFVo2UUEmgP5NftXNmZubPJ5CUJrIicnhzZt2pCSkuLR+BkzZvD888837aRqIOJJEISzFpvTxvt73gfg9n63Y1Ka/iNPtyloF1lP5Ck2BIDMPAtXdrsSgHd2vdPk8xKEurj11lu54oorWnoatZg7dy6XXXYZycnJHo1/4okn+Pvf/05hYWHTTqwKEU+CIJy1/JD2A1llWcQGxTKty7RmOeeJfC1tV1/NU8cYTTyl5ZZyc5+bAfjpxE8cLzreLPMThDOdsrIy5s+fz513er64Y8CAASQnJ7Nw4cImnFk1Ip4EQThr+fTgpwBc0e0KrGZrs5xTjzwl1lPz1D5aE09FFXbCzAmMbjcaQEwzzyZUFSpLWubhQ/3cuHHj+P3vf88DDzxAdHQ0CQkJ/Oc//6GkpITbbruN8PBwunbtyrJlyxo8zpIlS4iIiEBVVQ4dOoSiKKSnp+N0OgkNDWX58uUN7r9s2TIsFgujR492bVu0aBFBQUGkp6e7tt15550MGDCAgoICAKZPn86iRYsMX783WJrlLIIgCM1MenE669PXA3B196ub5ZyVdieniiqA+tN2QVYzCRGBnCysIDW3lKt7XM2GjA0sObSE+wbdh8VUx8dy4QnY+j70mQ5tejflJQj+wFYK/0hsmXM/egICQg3v/u677/LII4+wceNGPvroI+69916WLFnClVdeyaOPPsoLL7zAzJkzSU1NJSQkpM5jbN++nYEDB6IoCjt37iQ2NpakpCT27dtHaWkpAwcObHAOa9euZdiwYW7brr/+ev75z38yd+5cXnnlFZ566ilWrFjBzz//TGRkJAAjRoxg7ty5VFRUEBgYWNeh/YZEngRBOCv5/ODnqKiMbDeSDhEdmuWcJwvLUVUIMJuIDQ2od5yeukvNLeXiDhcTExRDVlkWa4+vdR/osMFPL8Erw2HNP2DVE005fUFg4MCBPP7443Tv3p3Zs2cTHBxMXFwcs2bNonv37jzxxBPk5OSwc+fOeo+xY8cOBg0aVOfr+Ph42rVrx9dff03Pnj3p3r07b731ltv+KSkpJCa6i09FUfj73//OW2+9xT/+8Q9efPFFli9fTlJSkmtMUlISFRUVZGZm+ueX0QASeRIE4azD7rTz+aHPAZjRfUaznTejyqagbWQQJlP9lggdYkLYlJJHWl4pVrOVy7tezju732HxwcXVKwKProWlf4KsfdU7ntpX9wGFMwtriBYBaqlz+8CAAQNcr81mM7GxsfTv39+1LSEhAYBTp07Ve4zt27czbZpWY7hjxw5XpEmPSNntdh566CFWr15NREQEQ4YM4aqrriImJgbQap6CgmrXDE6bNo0+ffrw1FNPsXLlSvr27ev2fnCwFu0tLW36ptsSeRIE4azjx/QfOVV6iujA6GaxJ9Cprnequ1hcp0N0ddE4wFXdrwK0eWcWHofP7oJ3L9OEU0gsTJyr7ViQqtW1CGc2iqKlzlri4aOPmdXqXhuoKIrbNt0nzems2xm/qKiIlJQUl+CqGXnaunUrgwYNYuPGjfTt25ekpCTCw8OZMmUKK1ascB0jLi6OvLy8WsdesWIF+/btw+FwuERcTXJzcwGIj4/34oqNIeJJEISzjsUHFgMwvet0Asz1p8/8TbrL46nueiedmmk7gOTIZIa3HY5TdfL5L8/Czo8ABYbfCb/bDKPv00QUQM6hJpu/IPhKRkYGAOHh4RQUFJCSksKgQYPIysrihx9+YPz48Zw4ccIt3da+fXu3QvDBgwezZ88et+Nu3bqVa665hjfffJOJEycyZ86cWufetWsX7du3Jy4uromurhoRT4IgnFVklmSyNl2rHbq6R/MUiutk5Ovu4g1HnnSvJ108QXV68bOTv+AAGHAdTH0OQrRUBnE9tOfsg36dsyD4k6SkJEJCQnj++edZs2YNVquV8vJyrrrqKkaMGMH48ePrdNSv6fw/ceJEdu/e7Yo+paSkMHXqVP7yl78wc+ZMnn76aRYvXsyWLVvcjrFu3TomTJjQtBdYhYgnQRDOKpYcWoJTdTI0YSidIzs367kbM8jU0SNPJ/LLsTm09MclnS4hMjCSTEcpPwUHQXQn953iumvP2Qf8O2lB8COhoaF88sknfP/991xxxRXYbDYmT57MqFGj+Oabb1AUhaSkJLdI0/Hjx2nXrp3r5/79+zNs2DA+/vhjcnNzmTx5MtOnT+fRRx8FYOjQoVx22WU89thjrn3Ky8v5/PPPmTVrVrNcpxSMC4Jw1uBwOlx+STN6NF+huI5ukJlUj8eTTnxYIIEWExV2Jxn55XSMDSHQHMj0rtN5f8/7fBoexgVRHd13iuupPYt4EvzIggULXK/XrFlT6/262qM01otxypQpTJkyhRtuuAGAhQsXukWWRowYwa5du0hPTyciIoKlS5fyxBPuK0nnzJnDww8/zKxZs9i7d2+tc3zxxRduP8+fP5+RI0cyatSoBufmLyTyJAjCWcOGjA1klGQQERDB+E7jm/38J/TIUyNpO5NJoUNM/am7tSHBnAoKd99J0nZCK2P//v0MHz68VjNui8XCc889x0UXXcTgwYP505/+RGxsrNuYKVOmcPfdd7tFqBrCarXy8ssv+23ujSGRJ0EQznxO7dOW7ocnQGQH7REaV2tl0acHNEfx6V2nE2huWpO80ymrdJBfagMaT9uBlro7dKrYTTx1iezMkIpKtgYGsKRgL3dxefUOetou5xA4HWAy+3X+guBP7HY7u3fvdrM+qMn06dOZPn16g8e4//77PT7fXXfd5dX8fEXEkyAIZz6f3gan3FffYA6EDiPgpsVgCSSvPI8f0n4Aqpf+Nyd61Ck0wExEUOMfra4ed3k1PGlKsri6sIit8bF8cWIts9Q/V39rj+qoXbO9HArSIDrZ35cgCH7DYrFQXl7e0tNoMlp92u61116jc+fOBAUFMXToUNatW1fv2FtvvRVFUWo9ahptLViwoM4xZ/M/AkE4o7GVwamqmofEIRDeDlDAUQEp6+D4ZgBWpKzArtrpHdOb7tHdm32a1SvtgmulKeqirrQd+WlcWlJKsKqSWpTGr9m/Vr9nMkNsN+21pO4EoUVp1eLpo48+4oEHHuCxxx5j27ZtjB07lsmTJ5Oamlrn+BdffJGMjAzXIy0tjZiYGK655hq3cREREW7jMjIy6nQ7FQShGcg5DKgQFAWzvoc/7oPHT0HyWO39vBQAvj7yNQDTukxrkWmeyG+4IfDpdIjWxqXVFE8FqYSoKher2nv6NbmQFXeCcEbQqsXT888/zx133MGdd95J7969mTdvHh06dOD111+vc3xkZCRt27Z1PTZv3kxeXh633Xab2zhFUdzGtW3btjkuRxCEutCFQlyP6honS0B1FCbvKGmFaezI2oFJMTG58+QWmaaetkuM9OyLVl1eT+SnATAtWFtpt/zocmxOW/X7rqJxEU+C0JK0WvFUWVnJli1bahliTZgwgfXr13t0jPnz53PppZfSqZO7n0pxcTGdOnWiffv2TJs2jW3btjV4nIqKCgoLC90egiD4iZriqSZ6zU9eCt8c/QaAUe1GER/S9K0Z6sKVtvOgWByqW7Tkl9ooKKsSSPla1HxUbF9igmLIq8hjw4kN1TvJijtBOCNoteIpOzu7zv42CQkJHnVUzsjIYNmyZdx5551u23v16sWCBQv48ssvWbRoEUFBQZx33nkcPFj/h9XcuXOJjIx0PTp0aJ4O7oJwTqCLp/jTxFOMZoCp5h7hmyOaeGqplB14blOgExpoIS5Max3jSt0VaJEnS3QyUzpPAU5L3elpu6z9fpixIAhGabXiSef0wkxVVT0q1lywYAFRUVFcccUVbttHjRrFTTfdxMCBAxk7diwff/wxPXr0aNA/Yvbs2RQUFLgeaWlphq5FEIQ6qDfypImn3UWppBSmEGwJ5pKOlzTz5KrRa54aM8isiV407hJPVWk7Iju6hODq1NWU2KqaAeupytJsKM31fdKCIBii1YqnuLg4zGZzrSjTqVOn6uy2XBNVVXn77beZOXMmAQENNw01mUwMHz68wchTYGAgERERbg9BEPyA0wnZVY1w60nbfW2xAzCuwzhCrCHNOLlqVFUlo0BP23m+uMStQbCquiJPRHWgT2wfkiOSKXeU813qd9r2wDCIaK+9ltSdILQYrVY8BQQEMHToUFatWuW2fdWqVYwZM6bBfX/44QcOHTrEHXfc0eh5VFVl+/btbn13BEFoJgrSwF4G5gCIOq3XW1AE9pBYloVpAqQlU3aFZXZKKx2A5zVPcJrXU3k+VFTVS0a2R1EUpnaZCsDXh2uk7uKlaFwQWppWK54AHnroId566y3efvtt9u7dy4MPPkhqair33HMPoKXTbr755lr76T1w+vXrV+u9p556ihUrVnDkyBG2b9/OHXfcwfbt213HFAShGdEFQkxXMNc2nvw5JpFcs5kYSyijE0c38+Sq0eudokOsBAd47vytp+2O5ZRWp+xC4iAgFMAlnn7J/IWs0iztfVlxJwgtTqsWT9dddx3z5s3j6aefZtCgQaxdu5alS5e6Vs9lZGTU8nwqKChg8eLF9Uad8vPzueuuu+jduzcTJkwgPT2dtWvXMmLEiCa/HkEQTsNV71S36eXXVU7ek0I7YTVZm2tWtfDW40lHT/FlFVW4pex0OoR3YFD8IJyqk2VHl2kbXV5PkrYTzi3S0tIYN24cffr0YcCAAXzyySctNpdW357lvvvu47777qvzvZrdonUiIyMpLS2tPbiKF154gRdeeMFf0xMEwRdcK+161nqr1FbK9858AKapLVPrpHOiwDubAp3oEK3mMrekskaxuPtq3WldprE9aztfH/mam/veLJEn4ZzFYrEwb948Bg0axKlTpxgyZAhTpkwhNDS02efSqiNPgiCc5WTVs9IO+C71O8pUB51sNvoVtuzKswxX5Mm7TgQxoZp4yi+1oeYf0zZGdXQbMzF5IhbFwt7cvRzOP1z9u8hLAXuFT/MWhDVr1pCcnOzXY+bk5NCmTRtSUlI83mfGjBk8//zzDc6tXbt2DBo0CIA2bdoQExNDbm7L/L8v4kkQhDOXBtJ2urfT1OISlPyUZpxUbTJ8jDxVOpw48qpKDE6LPEUFRXF+0vlA1TWHJUBgBKgOyD3q48wFwf/MnTuXyy67zCtR9sQTT/D3v//dY5PpzZs343Q6W8xXUcSTIAhnJqW5mp8RQKy7eMotz+XnjJ8BmFpcVWztsDf3DF2kG4w8BQeYCbJqH8NOXTydFnmC6sLxpUeXooL0uBPOWMrKypg/f34tA+rGGDBgAMnJySxcuLDRsTk5Odx888385z//MTpNnxHxJAjCmYkuDCLaa/5GNfj22Lc4VAd9Y/vSUTVrUZiCljOnzSgwVjAO1dEnU+FxbUNU7W/SF7S/gGBLMOnF6ezO2S11T0KTsWTJEiIiIlBVlUOHDqEoCunp6TidTkJDQ1m+fHmD+y9btgyLxcLo0dWrX/VuHenp6a5td955JwMGDKCgoMC1bfr06SxatKjB41dUVHDllVcye/bsRm2JmhIRT4IgnJnU15YFXCvPJiVPqtHjrmVSWE6nSqYBg0yd6JAAginHUl5VuxFZWzyFWEMY134cUHXtEnk6o1FVlVJbaYs8VFX1ae7bt29n4MCBKIrCzp07iY2NJSkpiQMHDlBaWsrAgQMb3H/t2rUMGzbMbdv1119Pz549mTt3LlBtCbRs2TIiIyNd40aMGMHGjRupqKi7lk9VVW699VYuvvhiZs6c6dN1+kqrX20nCMJZit6/7bRi8VOlp9hycgugFVMTvRSy92sF1C1AdkkFNoeKokBChPfiKSY0gEqlKj0ZGAHBUXWOm9R5EstSlrE8ZTl/7PsH7ZuviKczkjJ7GSP/N7JFzv3LDb/45LS/Y8cOV1H26a/j4+MbNYxOSUkhMTHRbZuiKPz9739nxowZJCYm8uKLL7Ju3TqSkpLcxiUlJVFRUUFmZqbLcqgmP/30Ex999BEDBgxgyZIlALz//vv079/f2MX6gIgnQRDOTHQfo9OKxVemrERFZVD8INqFtXM1CG6p4ulThdq35LiwQKxm74P5USFWLLp4qqPeSef8pPMJs4ZxqvQU280qQ0D7HakqeNDPUxA8Yfv27Uybprn179ixwxVp0iNSAF9//TV//OMfcTqd/PnPf3arbyorKyMoqPaXiGnTptGnTx+eeuopVq5cSd++fWuNCQ7W0t712Qmdf/75OJ1O3y7QT4h4EgThzMS10s7d42lZSlXKrvMkbYMrbZfSPPM6jfxSmzaNEGMmnTGhAUTq4qmOlJ1OgDmAiztezJeHv2RZ7q8MMVmgshiKMiAisd79hOYn2BLMLzf80mLnNkpRUREpKSmuSM6OHTu4+uqrAdi6dSuDBg3Cbrfz0EMPsXr1aiIiIhgyZAhXXXUVMTExgNZ3Ni8vr9axV6xYwb59+3A4HPX2n9VtB+Lj4w1fQ3MhNU+CIJx52MpB9z2qkbZLL05nZ9ZOFBQmdJqgbYyuijy1UM1TQZkmniKDjYmnqJAAklyRp4aXXU9K1gTjytRvseuiUVJ3ZxyKohBiDWmRh+JDFDIjIwOA8PBwCgoKSElJYdCgQWRlZfHDDz8wfvx4Nm7cSN++fUlKSiI8PJwpU6awYsUK1zEGDx7Mnj173I67detWrrnmGt58800mTpzInDlz6jz/rl27aN++PXFxcYavobkQ8SQIwplH7mFQnRAYCWFtXJtXpGgf0sPbDic+pOrbqSttl6KlsJoZX8VTTIiV9kpV37oGIk8AoxJHERkYSW55LptjqupFpE2L4CeSkpIICQnh+eefZ82aNVitVsrLy7nqqqsYMWIE48eP58SJE261Su3bt3dbRTdx4kR2797tij6lpKQwdepU/vKXvzBz5kyefvppFi9ezJYtW2qdf926dUyYMKHpL9QPiHgSBOHMo+ZKuxrfpJcf1ZZJu1J2UF0nVFmkeUM1M7p4ijAonqJDa0ae6q95ArCarIzvNB6A5QFVQlEiT4KfCA0N5ZNPPuH777/niiuuwGazMXnyZEaNGsU333yDoih1ruarGe3q378/w4YN4+OPPyY3N5fJkyczffp0Hn30UQCGDh3KZZddxmOPPeZ2jPLycj7//HNmzZrVtBfpJ6TmSRCEM4862rKkFKSwN3cvZsXMpR0vrR5rDYbwRCg6oaXuQmObdar5ZZUARAUHGNo/2ou0HWipu08PfMq3FZk8Bljzjhk6ryDUxZQpU5gyZQo33HADAAsXLnQTR0lJSW6RpuPHjzNypPvKwjlz5vDwww8za9Ys9u7dW+scX3zxRa1t8+fPZ+TIkYwaNcpfl9KkSORJEIQzjzrasixP0aJOoxJHER0U7T6+BYvGC31M28UGqbQhX/shsuHIE8CwhGHEBsVS4ChnQ3AQlJwydF5BaIj9+/czfPjwWjVUI0aMYNeuXaSnp1NUVMTSpUuZOHGi25gpU6Zw9913u4msxrBarbz88st+mXtzIOJJEIQzj2zd46l6pZ0rZZc8qfb4FrQrqK55MhbIj3FkYVJUytQA1JDGo2Zmk5kJyVpdyPLQUCjOMnReQagPu93O7t27GTBgQK33LBYLzz33HBdddBGDBw/mT3/6E7Gxtf/d3n///V71nbvrrrvo2bNn4wPPECRtJwjCmYXTCdmHtNdVabuDeQc5XHAYq8nKxR0vrr1PC664c4kng1YF0ZWZAKSrcbSzOQkNbPw77eTOk1m0bxHfhwZTkXeKQPF6EgySnJzMAw884LbNYrFQXl5e7z7Tp09n+vTpTTyzuud2piCRJ0EQziwKj4O9DExWVzpOb8dyXtJ5RARE1N6nBdN2ungyWvMUWKKlNtLVOPJKKz3aZ2D8QBJCEigxmfgx0Azl+YbOLQhnskA5k+cm4kkQhGbB5nCSmlOKw9mInYBeLB7bFcwWVFV1WRRMTp5c9z4tmLbTTTKNrrZTCrSGwOlqHHklNo/2MSkmV/pyWWgIFEvdkyA0J5K2EwShWXjii10s2phGeKCFYcnRjOgcy4jOMfRPiiTAUuN73GnF4nty95BalEqQOYhxHcbVfXA98lR0QjPYtHrfY84ovvo8kZ8GwHE1jiQPI0+g2TW8u+dd1oYEU1qQRkh866kXEYTWjognQRCaHFVVWbVHi44UVdhZvT+L1fu1QueY0AC++O15dIipamaa7W5TsOKoFnUa235s/Q1PQ2IhIFzzeso/Bs0kJBxOlaJyO+CLeEoF4LgaT08vxFPf2L60Vy0cN9lZm/4jk7pd2vhOgiD4BUnbCYLQ5GQUlJNdXIHZpPDZfWN4YlofJvVtS1ighdySSn48lF09uEZPO7eUXed6UnagFUvHJGuvmzF1V1RenWYzLJ4KNPGUrsaRW+K5eFIUhUlWrY3F8uytxs4tCIIhRDwJgtDk7DyeD0CvtuEM6RjN7ed35o2ZQ7l2mLaU+dCp4urBVWksopPZmb2TEyUnCLGEMDZpbMMnaYGicb3eKSTA7J569BSnAwpPAHrNk+fiCWBSeDcA1hUfo7iyuJHRgiD4CxFPgiA0OdvTCgAY0D7KbXu3NmEAHNTFk6pCsbZ0n/AEl7fTuA7jCLI0UsfUAnYFPtc7FWWA045DMXOKaPJKPSsY1+kR1ZXkShuVOFmdttrYHAS/4XQ6W3oKggf44+8kNU+CIDQ5O9LyARjUIdJte/cETTwd1sVTWR44tOiLM7QNK1NWAvUYY55OC0SefC8W11J2JUHtcJaZyPWi5glACUtgUkkpbwREsjxlOZd1vczYPASfCAgIwGQyceLECeLj4wkICKjlzC20PKqqUllZSVZWFiaTiYAAY/YiIOJJEIQmxulU+TVdizwN7BDl9l63eE08peeXUVJhJ7T4pPZGUCRbc/dwquwU4dZwzks6r/ETtYBdga9Ngam63srgNpAH+V6KJ8ISmFRSwhvRkaw/sZ6CigIiAyMb30/wKyaTic6dO5ORkcGJEydaejpCI4SEhNCxY0dMJuPJNxFPgiA0KUeyiymusBNsNbvEkk50aACxoQHklFRyOKuYAZVV4imsrauX3cUdLybA7ME3RFfaLkVzKffhg9FTqg0yDYqnsjztOSQGgFwPfZ5chMXT1Wanu13loMXO96nfc2X3K43NRfCJgIAAOnbsiN1ux+FwtPR0hHowm81YLBafI4MingRBaFL0eqf+SZFYzLUFTbc2YeQczeXQqWIGmDXxZA9vw6pjqwDNz8gjItuDYgZHhVY3FZHonwtoAJ/TdlXiyVQlnrwtGCcsAYBJRUUcjI5g2dFlIp5aEEVRsFqtWK0G/z0IrQYpGBcEoUnRV9oNaF93OsmtaLyqWHxTUAi55blEBUYxst1Iz05ktkJovPa6mRy3/SWeLKFV4qm0ElVtxIG9JlXXO6lYqxnbmLmR3PJcY3MRBMFjRDwJgtCk6MXip9c76eji6dCpYijSIk8rlFIALu10KVaTF8IkpKq7e2mOobl6S0Gpf8RTUITm11Rhd1Jm8yLlY7ZCcAwd7Xb6RHTBoTr49ti3xuYiCILHiHgSBKHJqLA72JNRCMCgesRT9zbhQNWKu+JMbMC3FVoEyqNVdjWpSn+5aomaGFfNU4hR8ZQPgDUsloCqlKa3dgWEtQFgUmx/AFetmCAITYeIJ0EQmox9GUXYHCrRIVbaRwfXOUaPPKXklOAszGRDcBAFzgpig2IZljDMuxMGR2vPpc2TuvJ5tV3VPJWQaKJDtWN4X/ekiaeJIZ0A2Jy5mVOl0ihYEJoSEU+CIDQZO6rqnQZ2iKp3dUtCRCDhgRacKtgKM1kRqvWvG99pPGaT2bsTuiJPzSOe8v1U80RwNNEh2opCb1q0ABCqiafEygoGxA9ARXUV2wuC0DSIeBIEocnYrtc7neYsXhNFUehaFX2qLDnJd1XiyeNVdjUJrhJPzRR5KmwC8ZRnwOsJgJJTTE7W+v8tPbrU2HwEQfCIVi+eXnvtNTp37kxQUBBDhw5l3bp19Y5ds2YNiqLUeuzbt89t3OLFi+nTpw+BgYH06dOHzz//vKkvQxDOSnYe180xGzZu7NYmjCAq2GB1UGIy0S4kgcFtBnt/wmaOPPm02k5V3cRTTGiVePI6bVe9wnBi8kRMiomdWTtJK0rzfk6CIHhEqxZPH330EQ888ACPPfYY27ZtY+zYsUyePJnU1NQG99u/fz8ZGRmuR/fu3V3vbdiwgeuuu46ZM2eyY8cOZs6cybXXXssvv/zS1JcjCGcVheU2DmdpS+hP72l3Ot3bhNFGyWdpWCgAkztPxaQY+HhqxtV2NoeT4go7AFEhBto82Mo0TyqA4GhX0bn3BeNVkafiU8SHxDOi7QgAlh1d5v2cBEHwiFYtnp5//nnuuOMO7rzzTnr37s28efPo0KEDr7/+eoP7tWnThrZt27oeZnN1XcW8efMYP348s2fPplevXsyePZtLLrmEefPmNfHVCMLZxa7jBagqtI8OJi4ssMGx3dqEEWvKZG2IVlQ+tetUYydtxrSdnrIDiAgy4DesR51MVggIq448eZu2q6p50r2tpnbRfnffHPnGO88oQRA8ptWKp8rKSrZs2cKECRPctk+YMIH169c3uO/gwYNp164dl1xyCatXu3ci37BhQ61jTpw4scFjVlRUUFhY6PYQhHOdHXrKrpGoE2h2BUrEXmyKQjfVQo/oHsZO2oxpOz1lFxZoqdM5vVFqpOxQFOMF41Wr7SjRxNMlHS8hwBTAkYIj7M/b7/28BEFolFYrnrKzs3E4HCQkJLhtT0hIIDMzs8592rVrx3/+8x8WL17MZ599Rs+ePbnkkktYu3ata0xmZqZXxwSYO3cukZGRrkeHDh18uDJBODuoNsdsvFFtUnQwBREpAIw3xRo/qSvy1PQ+T767i1cJvCp7Bd2qIN+gzxMlWeB0EB4QzoUdLgRg6REpHBeEpqDViied05c/q6pa75Lonj17MmvWLIYMGcLo0aN57bXXmDp1Kv/3f/9n+JgAs2fPpqCgwPVIS5NCTUFw2RR4EHnKLjvFqWBt/HClk/GT6pGnyiKwexnB8RJ/tWZxiSejkaeQOEAB1elKV07trKXulh5dilN1GpufIAj10mrFU1xcHGazuVZE6NSpU7UiRw0xatQoDh486Pq5bdu2Xh8zMDCQiIgIt4cgnMucKiwno6AckwL9khqPPC1PWQ4KDC4vx+n0/P/fWgRFAlVfdJrYZbypxJPXNU9mS3WhfLHW3ub89ucTbg3nZOlJtpzcYmx+giDUS6sVTwEBAQwdOpRVq9zN4FatWsWYMWM8Ps62bdto166d6+fRo0fXOubKlSu9OqYgnOvo9U7d24QTGth4MbXuSzSluJQjFWHGT2wy13AZb9oVd/4WT4YLxsHN6wkg0BzIpZ0uBcTzSRCaAgNLRM4cHnroIWbOnMmwYcMYPXo0//nPf0hNTeWee+4BtHRaeno67733HqCtpEtOTqZv375UVlbywQcfsHjxYhYvXuw65v33388FF1zAv/71Ly6//HK++OILvv32W3788ccWuUZBaI14U+90tOAoe3L2YFZhYkkpLyohvp08JEarJ2rionF/NQWurnnSxFO5zUlZpYPgAC/c1cPi4RSuFXegrbr7/NDnrExZyaMjHsVqNjhPQRBq0arF03XXXUdOTg5PP/00GRkZ9OvXj6VLl9Kpk1YzkZGR4eb5VFlZycMPP0x6ejrBwcH07duXb775hilTprjGjBkzhg8//JDHH3+cOXPm0LVrVz766CNGjhzZ7NcnCK2V3Se0yFN/D+qd9MjI6Ao70U4nO/ODGq0zbJBmsivwvSmwu3gKDTBjNSvYHCp5pZUEB9TdC7BOang96QxLGEZ8cDxZZVn8mP4jF3W8yNg8BUGoRasWTwD33Xcf9913X53vLViwwO3nRx55hEceeaTRY86YMYMZM2b4Y3qCcE6SmlsKQJe40AbHqarqWhE2tTAfgGOVEWQUlJMY5YV4qEkz2RX43BRYF08hmnhSquwKThVVkFtS6d31h+ou4yddm8wmM5M6T+L9Pe+z9OhSEU+C4Edabc2TIAhnJk6nSlpeGQAdYxpOwe3O2U1qUSrB5kAuLi3DgYlcwjl0qtj4BJop8uR7U+B87Vmv0cKHonFXzVOW22bdMHNN2hpKbCVGZikIQh2IeBIEwa9kFVdQaXdiNim0iwxqcOw3R74BYFzcYEJUlUJzNCom38RTM0eeDIunUnefJ6j2evK+RYvuMn7SbXOfmD4kRyRT7ijn+9Tvjc1TEIRaiHgSBMGv6Cm7dpFBDTpv25w2V73T1KheAFQEaemng/4QT00ceSr082o7wIfmwLp4co88KYrClM5aTeeXh780Nk9BEGoh4kkQBL+SViWeGkvZrTu+jtzyXGKDYjnPHKVtDGsLwOFWkLbzd8G4dixf+9udrPXWZV0vA+CXjF/IKM7wfp6CINRCxJMgCH5Fjzx1iG5YPH1x6AtAu7lbqmp1AqI1z7WDp4qMT6A1pO1sZWDX6sLcIk8hRiNPVTVPpTngsLu91T68PSPajkBF5YvDX3g/V0EQaiHiSRAEv5KWW1UsHlu/eMopy2Htca2n5OVdL4cizdU/PK49iqLV/OQUVxibQDNEnirtTkorHYBB8aQXiytmCKzuSKBHsXK9rXkKiQHFBKhQml3r7cu7XQ5oglVVVe/nKwiCGyKeBEHwK3rarn10/UvtvznyDXbVTr/YfnSL7uZKN1kj25FUtUT/cJbB1WHNEHnSo04A4UFGxFONlF0NPyu95inf27SdyVzDruBUrbcv7XgpodZQjhcfl3YtguAHRDwJguBX0vIarnlSVZUlh5cAcEW3K7SNeq1OeFsSIzXxdKqo3NgE9D5vZXngbJqmuC6PpyALZpMBM8866p2g2mXc6+bAUKPuqbZ4CrGGMDF5IgBLDi3x/tiCILgh4kkQBL9RYXeQWaiJng71iKe9uXs5mHeQAFMAkzpP0jYWVYmnsATiwjUBkV3kY9pOdUJ5vrFjNIKr3slwsXhtmwKo4fNkRDzpK+5KaosnqBaqK4+tpNRW6v3xBUFwIeJJEAS/kZ5XhqpCSICZ2KooyunokY9LOl5CZGAkqGp15CksgdjQQACyiw0ICABLAARUNRfWIzx+pilsCqBGwbi3NU9Qr9eTzqD4QXSK6ESZvYwVKSu8P74gCC5EPAmC4DdqrrSrqzddpaPS5e2kFzFTmgvOKrEQlkBcmCaeckoMRp6gyYvG88s0Yedv8RRVZZJZZnNQbnN4d8x6vJ50FEXRivNBVt0Jgo+IeBIEwW/obVk6xNRdLL46bTUFFQUkhCQwqt0obWOxttKO4BiwBLjSdllFBiNP4OoX11RF4wVVkaGo4Lqja41Sj3gKD7Rgqaqh8qfXk85lXS/DpJjYcnILaYVp3h1fEAQXIp4EQfAb+kq7+uqddG+n6V2nYzaZtY1VNgWEawaZ1Wm7MzfyVFCmeSn53BT4NPGkKIrxonFXf7u6a54A2oa2ZXS70QCuon1BELxHxJMgCH4jrQGDzFOlp/jpxE9AjZQduNU7AcRXRZ58Stu5Vtw1lXhqmpongOiqIvS8Em/729VvVVATvXD8y8Nf4nB6mRoUBAEQ8SQIgh9JbaA1y1eHv8KpOhncZjCdIjpVv1HDpgBqRJ58Stvpkacc48doAL/VPOnzrEG00RYteuSpEfF0UceLCA8IJ7Mkk18yf/HuHIIgACKeBEHwI/Wl7Zyqk88OfgbU8HbScdkUaDU7ceGaeCqzOSipcG814jFNnLbz32q7qFpvGRZPes1TWS446o9aBZoDXc2CFx9Y7N05BEEARDwJguAnCkptFJZrYuf0gvENJzaQWpRKuDWcScmT3HfUC8armgKHBpgJsmofTTlG7Qqa2GXc56bApQ2k7UJ1rycv03bB0WCyaK9L6l5xp3NNj2sA+D71e06VNhypEgShNiKeBEHwC7qzeFxYACEBFrf3Ptz3IaDVOoVYT0vp6ZGncC3tpCiKK3WXdYb2t2vKmqeYKrsCryNPJlONFi31r7gD6BnTkyFthmBX7Xx64FPvziMIgognQRD8Q30pu/TidH44/gMA1/W8rvaOp0WeoDp1Z7g5sMuqoGlMMn0ST/YKsFX17auzYNyXFi26eGo48gRwfa/rAfj0wKfYnAZMOQXhHEbEkyAIfiG1npV2H+//GBWV0e1GkxyZXHvHIveCcYD4sKoWLYbTdlWr7ZrKJLPUB/FUll/1QoHAyFpvG655ghpF4w1HnkBrFhwbFEtWWRbfp37v/bkE4RxGxJMgCH6hrobAFY4KV6H4db3qiDpVFFVHYfQbP37wegqusdpOVY0dox7KbQ4q7FrDYUO97WoWi5tqfwTrdVR6dMsrGulvVxOr2crVPa4GqtOqgiB4hognQRD8QmpubXfxFSkryK/Ip21oWy5sf2HtnfRl9QFhEBjm2qy7jBtP21WJJ0cF+LkJrr7SzqRA2Gm1XR7hEk+1bQqgOpqV71N/O8+KwK/pcQ1mxczmk5s5mHfQ+/MJwjmKiCdBEPzC8TrSdh/t+wiAa3tci8VUh9DQ3cVrRJ0A35sDB4SBqSoq5OfUnR4Rigi2YjLV7t/XKA0Ui4OPkadQ78RT29C2XNThIgA+2v+R9+erh7TcUv70yQ6ufO0nVy2cIJxNiHgSBMFnnE6V466+dpp42p2zm53ZO7GarFzV/aq6dyyuWzzpBeOGV9spSpPZFeQ34Uo7qG75Ulhuw+n0MuUYGqc9l2Z7vIteOP7V4a8oriz27nyncbKwnDlLdnHxc2v4ZMtxtqXm89qaQz4dUxDOREQ8CYLgMyeLyql0ODGbFNpFBgHVdTQTkicQGxxb946n2RToxIX5mLaDJisar24KbFQ8Vc2nHvGkizJVhaJyL01CdfFU4rmz+oi2I+gS2YVSeylfHfnKu/NVUVxhZ+7SvVzw7Gre//kYNofKwA5RACzemu7b31EQzkBEPAmC4DOpOVpqJikqGIvZRH55PsuOLgPg+p7X179jHTYFAHFhPqbtoLqmyM+Rp5ppO0M0EnkKtJgJtprdzuUxId5HnhRFcVlIfLjvQ1QDBfZPfbmbN9ceocLuZGinaBbNGsWS+8YwsH0klXYnH/yc6vUxBeFMRsSTIAg+k5bnXiy+5NASKhwV9I7pzcD4gfXvWG/kSRNPBWU2KqtWtnmN7vXURDVPTZW2g+q6J72Hnse4Ik/Z4PT89za963SCLcEcKTjCpsxNXp3S6VT5dq/2d/z3jAF8es9oRneNRVEU7hjbBYD3f06h3CZNiIWzBxFPgiD4TM2GwDaHjQ/2fgBoppiK0kBRte5HdFrkKSrYirmqGNuQWSQ0mct4c4gn/diGI0+qA8rzPd4tLCCM6V2nA7Bg9wKvTnngVBF5pTZCAsxcMTjJ7e89uV9bEiODyC6u5MvtJ7w6riCcyYh4EgTBZ/SVdu2jQ/j6yNecLD1JfHA807pOa3hHfVWYvsS+CpNJISZUN8r00a6gidJ2zSGevLYrsARUG2+Wel73BHBzn5sxKSbWpa9jX+4+j/f7+bB2nqGdorGa3W8pVrOJW89LBmD+j0cNpQQF4UxExJMgCD6T6hJPgby9621AuxkHmgMb3tEVeUqo9VZ13dOZ1d/O56bAungKqdvnCXyIPAGEVhXKN9Ic+HQ6RnRkYqeJAMz/db7H+/18RPv9jupS96KA64Z3JCTAzP6TRfx4yPNaLEE4kxHxJAiCz+ju4icdm0kpTCEiIIJrel7T8E4Oe3V05LTIE1SvuPO5RUsrjjwZE09V/e1KvBcqd/S/A4CVx1ZyrPBYo+OdTpVfjmp/w/rEU2SwlWuHdQDgrXVHvZ6TIJyJiHgSBMEnym0OThZWACrLjy8E4IbeNxBqDW14x9IcQAXFVC10auBz5CnkDK15KvW8YNyQeDKw4k6nZ0xPLmh/AU7VyTu73ml0/MFTxeSV2gi2mhnQvnafPp3bz+uMosAPB7I4cLLI63kJwplGqxdPr732Gp07dyYoKIihQ4eybt26esd+9tlnjB8/nvj4eCIiIhg9ejQrVqxwG7NgwQIURan1KC8vb+pLEYRWiW6OGRp5mIP5+wm2BHNjrxsb31FP2YXEgslc622fvZ5q9rfzIz5ZFThsUFklHjyqeTIQdXOl7YylyGb1nwXAF4e/4GRJww2Gfz6i/W6HJdeud6pJx9gQJvbRFgW8/aNEn4TWT6sWTx999BEPPPAAjz32GNu2bWPs2LFMnjyZ1NS6PUXWrl3L+PHjWbp0KVu2bOGiiy7isssuY9u2bW7jIiIiyMjIcHsEBQU1xyUJQqtDb78RFL8GgBk9ZhAVFNX4jnrz2jrqnQBiffV6chWM5xnbvx7yXSaZAd7vXJZf/Tqo/khNZIh27OZO2wEMajOIoQlDsTvtvLvn3QbH6uKpvpRdTe4c2xmAz7alG48mCsIZQqsWT88//zx33HEHd955J71792bevHl06NCB119/vc7x8+bN45FHHmH48OF0796df/zjH3Tv3p2vvnJ31VUUhbZt27o9BEGom7S8UszBKVRaD2ExWbilzy2e7VhcVdCs3+xPw28F4xWFWsTHD6iq6moMHGmkYFwXckGRdUbbdHyqefIhbaejR58+PfAp+fVYHmj1TnqxeP3F7zpDO0XTP0kzzVy5u+GIliCc6bRa8VRZWcmWLVuYMGGC2/YJEyawfv16j47hdDopKioiJsb9f/zi4mI6depE+/btmTZtWq3I1OlUVFRQWFjo9hCEc4XUnFICYtcAcHnXy0kIrTuSVIuSum0KdHwuGA+OAqo8h/wUfSq3Oal0aOaThmqePCgWh+rWL15bFUANo0zvVtvVZEziGHrH9KbMXsbCfQvrHHPwVDG5JZUEW830T4pq9JiKonBJb+1v/ZOsuhNaOa1WPGVnZ+NwOEhIcP+gTkhIIDMz06NjPPfcc5SUlHDttde6tvXq1YsFCxbw5ZdfsmjRIoKCgjjvvPM4ePBgvceZO3cukZGRrkeHDh2MXZQgtEL25e7DEr4PBRO39bvN8x11j6emijyZzFUCCr8VjeuRILNJITSg/shRvbjEU8ORGl2YFRpK23nf3+50FEXhzv53AvC/vf+jxFZSa0zNeqcAi2e3krHdtbn9dDjb+6bHgnAG0WrFk87p7sWqqjbsaFzFokWL+Otf/8pHH31EmzbV33xHjRrFTTfdxMCBAxk7diwff/wxPXr04OWXX673WLNnz6agoMD1SEtLM35BgtDKOFC5BIBBMRfQKaKT5zvWY5Cpo4un3JJK4zdaP/e3cxWLB1k8+pyphaeRJ1d7lpZJ2wFc0vESkiOSKaws5H97/1fr/cYsCupiQPsowgIt5Jfa2H1CIvRC66XViqe4uDjMZnOtKNOpU6dqRaNO56OPPuKOO+7g448/5tJLL21wrMlkYvjw4Q1GngIDA4mIiHB7CMK5wPZT2ymzbkNVFW7qdYd3OzdSMK47jDucqjERATXsCvyz4q6ovGmbAuvokafSSof3vf0M9rc7HbPJzN0D7wZg/q755JZXC1BVVV3mmCM7N17vpGM1m1xiSwwzhdZMqxVPAQEBDB06lFWrVrltX7VqFWPGjKl3v0WLFnHrrbfyv//9j6lTpzZ6HlVV2b59O+3atfN5zoJwNqGqKv/c+CwAtvzhjO7Q17sDNFIwHmAxuUTEmeIyXlRuByA8yGLsAHoErBHxFB5ULc6aq79dXUzpPIU+sX0osZXw2vbXXNv1eqcgq4kB7aO8Oub53XTxZLwmSxBamlYrngAeeugh3nrrLd5++2327t3Lgw8+SGpqKvfccw+gpdNuvvlm1/hFixZx880389xzzzFq1CgyMzPJzMykoKDANeapp55ixYoVHDlyhO3bt3PHHXewfft21zEFQdBYcWwFu3N+RXUGEFQy2e2G7xGu1ix1p+2gZtH4mdHfrrAq8hQe2LSRJ7NJIaJKoHktnnzob3c6JsXEw8MeBrSVd0cKjgA16p06xXhc76RzfndNLG9KyaPc5vBpfoLQUrRq8XTdddcxb948nn76aQYNGsTatWtZunQpnTppdRcZGRlunk9vvvkmdrud3/72t7Rr1871uP/++11j8vPzueuuu+jduzcTJkwgPT2dtWvXMmLEiGa/PkE4U6l0VDJvyzztdc4FdIjwcIWdTs3WLKH1iyffvZ6q6nHOmMiTZ+IJqq0QCsp8Mcr0PbozvO1wxnUYh0N18MKWF4Ca/k6ep+x0usaH0jYiiEq7k00p/nV/F4TmwuAnwJnDfffdx3333VfnewsWLHD7ec2aNY0e74UXXuCFF17ww8wE4exl0b5FpBenE2qOoSjnAtr3CfHuADVbs+g1OnUQXyWejLuMV4kUP0WeqsVT00aeQDPhTKPMuNdT7hHDRpmn8+DQB1l3fB1r0tawMWMjvxzRovXeFIvrKIrCed3iWLz1OD8eymZs97rTtoJwJtOqI0+CIDQ/BRUFvLnzTQD6BF0LagDto4O9O4heLF5PaxYdv6XtSv3j86QXjDdL5MkfzYF9XHGn0yWyCzN6zADgHz//m5ySckP1Tjq6ZcGPB+uZn6pq0UlBOEMR8SQIgle8ufNNiiqL6B7dHWupls72Wjzp9U4NpOygRtquyKhRpr9X22k39AhfxVNI4+kuPW1nzCjTt/52dXHvwHsJtYZyuHAflogdDO3kub/T6YypKhrffaKQ3JIaf9uCdFjzL5jXH/6vG5zc7Y+pC4LfEfEkCILHpBWmsWjfIgAeHvow6QVaw+z20V6m7fSVdmENp2x0r6eckjOjYLw68tT0aTu/tGjxo3iKDY51GWcGtlnB0OQww8dqEx5Er7bhAPx08CTsXwb/uw7m9YM1/4CCNO139fEtUFHkl/kLgj8R8SQIgkeoqsrcjXOxO+2cl3geY5LGcDyvDID2MQbTdvV4POnoabsswy1aziCrAqcDyqtW9nohnoxFnvybttO5qfdNmJ3RmKz5pDm/9ulY53XTBF7Smj/CouvhwHJQndDpfLj8VYhIgpyD8NX9WhpPEM4gRDwJguARXx7+knXp67CarPxp+J8oKre5buxJUd6m7RpuzaJTnbYzGnmqSl+V5fnlBuxK2xnqa5df/TooqtHhUX5p0eJfL6UgSxDO7MsA+D7zQ/bk7DF8rPO7x5FINoPyV2obRv8OfrcZbvsGBt8EM94BkwV2LYbNb/tj+oLgN0Q8CYLQKCdLTvKvjf8C4L5B99E1qivp+VrUKSrEasDjqeHWLDrxNdJ2qhHxo6ft1BpRHx8o9KVgXE/ZBUaAufH9XZEnQ2k7vebJP7VeOvmllRTm9MFW2B+n6mDOT3OwOYy5v4/sHMMM64+YUClLGgMT/w5x3asHdBwJl/5Ve738L3Biu8/zFwR/IeJJEFojlSXw04uw/X/akvQmTGuoqsrTPz9Nka2IfrH9uLXvrQAcz9XEk9dRJ6hO2zVSMB4XrqXtym1OSioNGCpaAsFaVY9V5vuKO5+sClz1TlEeDY8KOXNW2+kcyykFIKLkGqIDozmQd4D//PofQ8cKsZr5TcCPAGyLmVz3oNG/g55TwFEJn9ziFwEsCP5AxJMgtDacDvj0Dlj1BCy5F14aDM/1hI9vhp/fAFuZX0/35eEvWXt8LVaTlb+d/zcsJi1qcjxPu5F6vdIOahSMNyyeQgIsBFs1KwPDqbugKrftCt8b0foUedJbpXiQsoPq1KAx8eSf/nank5JTAkByVFseHfUoAG/tfIu9OXu9P1jaL7RznKBEDeSj4iF1j1EUuOI1iOoIeSnwxW+l/kk4IxDxJAitjZVz4MAysARB+xFgsmpL//d8Acv/DJ/N8tup6krX6ehpO69X2kGNgvGGxRNUR58Mr7jTxZOPUQunU6W4woeCcf38+nwaISpYu25DBeN62s4P/e1qkloVeeoYG8Kk5EmM7zQeu2rn8Z8e9z59t30hAEsdI1l9tASHsx5RFBwN1yzQ/p3v/QoOf+fDFQiCfxDxJAitiU3z4edXtddXvA53roLZaXDbMrjocUDRbjCn9vl8qvrSdTqulXbeRp4c9uol9I2k7QBiQ7W6pyyjXk9+Ek8llXZX0CPCSNrOS/Gk+zwVltm8r/eyBPqtv11NjuVq4ik5VhPMj418zFj6rrIUdn0OwDeWiykst/NregN/n6ShMFyzSeCnlwzNXRD8iYgnQWgtHPoOlv5Je33x49DvKu21NRg6jYEL/wS9pmrb1r/s8+k+P/R5nek6nWrxZLA1C0p1hKQBfPZ68pN40uudrGaFQCPmkF5HnjTxVOlwUmakga4f+9vpHKtK23WMDQU076ea6btd2bs8O9C+r6GyCKKTCex8HgDrDzdSnzX6PlDMcPQHKR4XWhwRT4LQGji1Fz65VUvDDPwNjH247nHnPaA97/wICk8YPt2OrB387ee/AbXTdTqGa55cxeJxHq06i69K2xl2GfezeAoPsqIoivcH0GuuPBRPIQFmLCbtPGeKUaZeMK5HngAmJU9iQqcJ2FU796++n6xSD8RaVcqOgTcwuptW3L7hcCMRsqiO0PdK7bUfvhwIgi+IeBKEM53SXPjftdrNt+MYuOxFrZC2LjoMh07ngdMGP79u6HSZJZk8sPoBbE4bF3W4iNv73V5rTHGFnTzd48nr1iyerbTT0dN2hvvb+U08+djXTj9/YIRHwxVFOaOMMksr7ZyqKtrvFBPq9t5TY56iS2QXTpWe4oHVD1DhaOBvlZ8GR37QXg+8njFVZpmbUnKpsDcSYTvvD9rz7s8hP9XQdQiCPxDxJAhnOmvmajeK6M5w3QdaPUtDnHe/9rz5HXdjRg8ot5dz/+r7yS7LpltUN+aOnYtJqf0xkV6VsosMtnpf/+PyeGrYIFNHdxk/U9J2xsWTd5EnqK57Mrbizr/97VKr6p2iQqyueemEBYTx8sUvExEQwc7snTy1/qn667R2fgiokDwWojvRvU0YcWEBlNucbE/Nb3gS7QZC5wu1CKzBLweC4A9EPAnCmUzO4Wp35cterL4hNkS38RDfW6sp2fKOx6dSVZUn1j/Bnpw9RAVG8fLFLxNqDa1zrE82BR56POnEhfvYHNhP4sllUxBosK+dq+bJs8gT+Niixc9pu5Rs7W/eKabuGreOER15btxzmBUzXx35ivf2vFd7kKpq3mQAg24EtAjb6K7aXNc3lrqD6ujTlnf94t0lCEYQ8SQIZzLf/w2cduh2KXS50LN9TKbqG8zPr4Pds4jN/F3zWXZ0GRbFwvPjnqd9ePt6xxpeaQceu4vrnDlpO701i8HIk5c1T+Brixb/pu1Sc92LxetiVLtR/Gm4tqjh+S3Ps+74OvcBab9opq4BYdBnumvzmK7al4JG654Aul4CCf3AViJtW4QWQ8STIJyppG+B3Z8BClz6lHf79puhNVYtPqkVjzfCypSVvLRVWwL+lxF/YXjb4Q2Or448GfF48swgU8dVMN7C4qnaINPHyJOHNU9QHXnyzSjTP6vt6ioWr4sbet3AVd2vwqk6eWTtI+zP3V/9pl4o3ucKCKgWYbp42paWR2mlveGJKAqM+b32+pc3Pf5yIAj+xCfxZLPZSEtLY//+/eTm+qdruSAIaOmNVU9qrwdeD237ebe/JQBG3ae9/umlBl2mvznyDY+sfQQVlWt7XMt1va5r9PC+RZ5Oas9eFowXltsbLyiui1Zc8xQVUmWUWWYgZenn/na6eOpYT9pOR1EUHhv5GEPaDKHYVsztK26vtjA4vEZ71m02qugYE0JSVDA2h8rmFA9ScX2vgvBEj78cCIK/8Vo8FRcX8+abbzJu3DgiIyNJTk6mT58+xMfH06lTJ2bNmsWmTZuaYq6CcO5w6DtIWQfmALjoUWPHGHqLZpSYcxD2L61zyOcHP2f2utk4VAfTu07n0ZGencuwxxPUaM3iWcF4ZLDVtWQ/t8SAiPD7arvmq3nyrUWLf9N2x6rSdslx9aftdALMAbx8ycsMjB9IYWUhs1bOYtux1VBQtUKuvXtkU6t70sSeR3VPlgAYda/2ev3Lfm1BIwie4JV4euGFF0hOTua///0vF198MZ999hnbt29n//79bNiwgSeffBK73c748eOZNGkSBw8ebKp5C0KrJ7u4gudX7uf/Vuzni+3p7M0o1CIrTgd8WxV1GnGX5m9jhMBwGHab9nrnh7Xe/mjfRzyx/glUVK7pcQ3PnPcMZpPZo0P7pWA8LMGj4SaTQmyYD15Pei85f9U8GYk8OexajU7N+XiAb1YF/utvV2l3ulZY1lcwfjoRARG8Of5NhiYMpdhWzN1rH2ZTUCDEdq9TQFbXPXko9obeqqVAsw/AoVWe7SMIfsKrT4H169ezevVq+vfvX+f7I0aM4Pbbb+eNN95g/vz5/PDDD3Tv3t0vExWEswWHU2XRxlSeXb6PwnL3+g6zSeHOiF+YXb5Li5iM/aNvJ+s5BX6aB8fWa6nAKn+o93a/x783/xuAm3rfxCPDH/HY+LHEF48np6O6XYiHaTuA6JAAThZWkFfqQ+SpolA7v4cC8XR8StvVbEocGO7xblG+RJ5O728XEuP9MapIzy/DqUKw1Ux8eCNWGTUItYby+qWvc//397MhYwP3JsTzYmgXzqtjrB55+jW9gIIym0s41ktQhBZdXf+y9ugx0YsrEgTf8Cry9Mknn7iEU1FRUb3jAgMDue+++7jzzjt9m50gnGXsSi/gqtfX8/iSXRSW2+mbGMFvRnRgaKdowoMsWJwVzCz7AICjve726YYHQOJgsARrgiVrPzaHjWc3PesSTnf0u8Mr4QTVDYENeTyVZIPqxNPWLDpRVb5ChsRTzQLtmiLGS3xK2+lRL2somD3f36eCcT/2t0upasvSKTbEa3f1YEswL1/yMhcqYVSYTPy+fD8f7/+4lg9Uu8hgusSF4lRh41EPa2hH3K21bElZBxk7vJqXIPiC4YLxsWPHkpmZ6c+5CMJZS6XdyV+/3M30V35kR1o+4YEW/npZH7747XnMvWoAi+8dw84nJ7BpQgrtlWxOqDHcsHMgJ6qEimEsAZrrOJB+cCm3LL+F9/e8D2htV+4fcr/XN0O/pOxCYj1qzaITXVU4bUxEBIC1KtXkQ+rOp8iTgXonqBaNhq4b/NbfLtXDYvH6CDQF8MKpHCYUl2BTnTzz8zM8svYRiiuL3cZV1z15mLqL6lDdsmXDq4bmJghGMCyehg0bxsiRI9m3z717+7Zt25gyZYrPExOEs4Vym4N7P9jCgvUpOFWYPjCR7/54Ibee1xmLufp/QaUsj4iNLwDwUdjNZJQq3Ltwq7EVZjXpdB7fhQRzzaH3+DX7V8IDwnnxohe5d+C9hnq0+cfjybN6Jx1X5KnEoIjwQ9F4zd52XmPA4wl8rHkCvxllumwKPCgWr5PCE1iLT/Lv7Hz+OOj3WBQLy1OWc93X17E3Z69r2Jgqs0yP/J50Rv9We961GArSjc1PELzEsHh66623uP322zn//PP58ccfOXDgANdeey3Dhg0jMNDznLggnM2UVtq5893NfLfvFIEWE/+9eRgv/WYwbSKCag/+8Xnt5t6mL1ff+jCRwVZ2pOXzt6/31h7rIeX2cv5lP8EDCfEU4WBAXH8+vexTLu54seFj+rTSrsS7lXY6Pi3ZB7+Ip0JfetsZ8HiC6vYsheU2nM562p00hJ9W3B2rStsZjTxxYisApjZ9uHXgXSyYvIB2oe1ILUrlxqU38r+9/8OpOhnVRUtT78ss8tzXK2lIVT9HO2z8j7H5CYKX+OTz9OSTT/LHP/6R8ePH069fP8rKyti0aROff/65v+YnCK2WonIbt769iR8PZRMSYGbBbSMY36eeiEveMc3wD2D803SMD2fedYNQFHj/52N8vu24V+dWVZWlR5Yyfcl0PkhfDcAtBYUsGPEEiWGJvlyWK22XFNX0Hk86Ub5GYHwUT06nSnGFP9J2xiJPqgpFFY2YR9aFn/rbHcvVDTINRp5ObNOeEwcBMDB+IJ9c9gnjOozD5rQxd+NcbvjmBlJKdtGrrVZQ71306Xfa85Z3oKK44bGC4AcMi6eMjAz+8Ic/8Mwzz9CnTx+sVivXX389Q4YM8ef8BKFVkl9ayU3zN7IxJZfwIAvv3zHSVc9RJ6v/Do5Krelpt0sAuKhXG35/sbZadfZnv7I3w7Ni5+2ntnPTspv487o/k1GSQUJIAq84Yng4Nx9rmu8ebM3ZmkVHr3nKN1IwDj6Lp5JKO3p9s9dF8lDDINO7yFOgxUywVVsdWNBC/e2cTtXVFLhTI+7i9ZKuRZ5Iqr4/RAZG8tJFL/GXEX8h1BrK7pzd3Lr8VmjzHoo1xzO/J50ekyC2m/b31V3MBaEJMSyeunTpwrp16/jkk0/YsmULn332Gffddx//+te//Dk/QWh1ZBdX8Jv//sKOtHyiQ6wsmjWKoZ2i698hY0e1S/L4p112AgD3X9KdC3vEU25z8viSXQ2ed1/uPv70w5+YuWwmO7N2EmwJ5veDf89XV37FhZ00Qcax9b5enn/SdqHepe0iXavtWibypFtKBJhNBFkNWB0YjDyBry1afE/bZRaWU2l3YjEptIusI93cGKpaI/Lk/uVaURRu7H0jX1/5Ndf0uAaTYiLd9guhXZ7n25P/JaM4w7NzmEzVjvo/v6ZZUghCE2JYPL3zzjts27aNqVOnAjBx4kRWr17Niy++yH333ee3CQpCayI9v4xr39jA3oxC4sIC+fCu0fRLauCGqaqwco72uv+1rrSGjtmk8O8ZA7CYFLYcy6sVfap0VPL1ka+5aelNXPPVNSxPWY6CwlXdr+KbK7/hrgF3EWwJhk5jtB2O/ejT9ZVU2F0u3157PIHhgnGfVtuBz+KpyJd6JzBcMA41isaN1Hv5ob+dblPQISbEbYGDx+Qd1XymzAHQpk+dQ+KC43hi9BN8etmnjGg7CsXkoDxkNZMWT+IP3/+B9enrcaqNGH0O/A0Ex0BeCuz72vt5CoIXGBZP119/fa1tQ4YMYf369axZs8aXOQlCq+RIVjHXvL6eI9klJEUF88k9o+nZthFDxMPfwdEftBvLxY/XOaRNRBAT+7YF4H+/pOJUnezO3s28LfMY/+l4Zq+bzY6sHVgUC5OSJ/HxZR/z1JiniA+pEd3pMFLzw8lPhfw0w9eoezxFBFkaNzGsC5d48rZgXK95apm0ne997YwVjEN11M0no0wf+tv5alPgStm17a/ZRjRA9+juvDXhPySV/x57SVecOFmdtpq7v72b6Uum886ud0gtTK1754AQGH6H9nr9K8bmKggeYvCToH6Sk5P56aef/H1YQTij2X2igFve3kh2cSVd4kP54I6RJDZWUO10VDf/HXEXRHeqd+g1w9qw/Oh3fJ72OT9+fJjs8uo0TJuQNlzT4xpm9JhBXHBc3QcIDId2A7VVT6kbNH8cA1R7PBm8keo+T94WjNcQEE6nisnkpcWC3yJPvva18yHyZKhFi+9pu+picaMr7fSU3WCPhiuKwow+l/K3b5IY0Lmc0YMO8OXhLzlWeIzntzzP81uep3NkZy5sfyEXtr+QQW0GYTFV3cqGz4KfXoTjG+HAiiZxHS8st/HZluMcOFXMqcIKsooryCosJ7u4kvAgC13iQ+kcF0qX+DA6x4UysH0UbY2kO4UzGq/EU2pqKh07Nt5nKzpaq+9IT08nKSnJ2Mw85LXXXuPf//43GRkZ9O3bl3nz5jF27Nh6x//www889NBD7N69m8TERB555BHuuecetzGLFy9mzpw5HD58mK5du/L3v/+dK6+8skmvQ2i9bE7J5bYFmyiqcgx/7/YRxIZ5YNfx04twsnYbFlVVOVZ4jF+zf2VX9i52Ze9ib+5eQjpoN8/scgixhDAmcQxTu0xlXIdx1TePhug0RhNPKT/CgGsNXatPxeI1W7N4WTAeFaxFLJyqFgXSozEec6ZEngyIJ59atJze387kfbLBZVNgdKWdHnlK9Hwx0ZT+7fjbN3v5NSWI//7mQe4fcj9fH/malcdWsiVzC0cLjnK04CgLdi8g1BpK39i+9I/rT/+4/vQbdgsJv/wXlv8FuozTnNb9wKnCct7+KYWFPx+rd+VjTkklOSWVbErJc9veJS6U0V1jGdM1jlFdYjz7fBDOaLz6JBg+fDjTp09n1qxZjBgxos4xBQUFfPzxx7z44ovcfffd/P73v/fLROvio48+4oEHHuC1117jvPPO480332Ty5Mns2bOnTpF39OhRpkyZwqxZs/jggw/46aefuO+++4iPj+fqq68GYMOGDVx33XU888wzXHnllXz++edce+21/Pjjj4wcObLJrkXwAYcNKoqgsgScNrAEVT0CtWeDvcwaw+lUeWd9Cs8u30eF3cnw5Gjm3zrco9VYlSk/kv3DXLICA0gbfgPHDiziWOExUgtTOVZ4jGJb7eXW4ZZ4ck51IylwKMvuupVAb28KyefDhld8Khr3qVi8NKdGa5Z6ImT1EGAxERpgpqTSQV5pZbOLp0JfxZMfap4KW6i/ncsg00jkyemobpuS5Ll4SowKZkjHKLam5rPs1wxuPa8z1/a8lmt7XktRZRE/nfiJH9J+YF36OgoqCtiYuZGNmRtd+8d06kCnymI6fnE9yT2m0jG8I0nhScQHxxMTFOPZl40qUrJLeHPtERZvOU6lQ6u76pEQxqR+7UiICCQ+LJA2EUHEhgZQUGbjcFYxR7JKOJpdwsFTxezPLORIdglHsktY+ctO+puO0DfSRp9Yha6R0CHMSbBaoX1eBUVqj8AI7TksHsITtS8bTfQ5JhjDq0+CvXv38o9//INJkyZhtVoZNmwYiYmJBAUFkZeXx549e9i9ezfDhg3j3//+N5MnT26qeQPw/PPPc8cdd7h66M2bN48VK1bw+uuvM3fu3Frj33jjDTp27Mi8efMA6N27N5s3b+b//u//XOJp3rx5jB8/ntmzZwMwe/ZsfvjhB+bNm8eiRYua9HrOJlRVxeZQqXQ4sdmdVDqcVNqdVNidVNgdVNq1nysdTuxOFafNhlpZjFJZjKmyiGB7AYG2AgIr8wm0FxBUmU+IQ3u2VuZhLs9FKcuHymJtiX9DBEZCXHeI7wlxPbTndgMhomG/I1VVcagO7eF0YHPacKgObA4bqXlF/H3pTnam54DFwYjuYdx1YSgbMr+nzF5Gmb2MElsJhRWFFFZWP3LKcsguzSK/sgA6aHVMHP8GTrNxCjQH0jumN/3i+rm+UYea2jDqn99zxO5kX0YZAzt4KZ46jgIUyDkIRSch3LuibdBuJAAdYnzwePKyNYtOVEgAJZVl5BsREWdK2s5AzVN1vZcP/e0qCjTx6qV4UlXVJZ4M2RRkHwBbidbTL66HV7tO6d+Oran5fFMlnnTCA8KZlDyJScmTcDgdHC44zK7sXezM2smu7F0czD9IrslJblAQ24oPwdYX3Y5rUkzEBMUQHxxPdFA0EQERRAREEB4QTkRgBGHWMIIsQQRbgvk1rYw31xzHZjeDxUL/DtHMHNmVC7u3I8BixWwyY1EsWEwWzIqZ9tHB1QtEVBUyd1J2aAcFB9YTeHIr0ZVVqwfL0P6f99S+TTFriywi2kF4Owhvqz3Cqp5DYiE4WnsERbqt2BWaBq8+wWJiYvi///s//va3v7F06VLWrVtHSkoKZWVlxMXFceONNzJx4kT69evXVPN1UVlZyZYtW/jLX/7itn3ChAmsX1/3N+sNGzYwYcIEt20TJ05k/vz52Gw2rFYrGzZs4MEHH6w1RhdcdVFRUUFFRbUbbmGh9i1z2nsjsAS3tm8LCnX7GNfertZ4r9Y29fS31Bo/qm7PJlS3ozWKGQgFNTQIqFlLoKAqCioqqKDW+PxQyUDNzUDNXQMHtLOpJgtOkwXVZEZVwKmqOFWn66E2NqdACO2ivdwLPPiD55cAYFEhPjSBxPD2JEck0zGiI50iOtEpvBOdIjthNdW+UU/t347Pt6Wz8JdjDOwQ5d0Jg6MhoR+c/BVS11f3BPOCQ1laRKxbmzCv9zXq8aQTGWwlPb/MWHPgFk/b+R558qm/XUWBtuIurrtXu+aWVFJcYUdRDEYb9ZRdu4FeR0701N3mY3mcLCwnoQ5XfrPJTI/oHvSI7sFV3a8CoNRWSkrBUY59eS/HCo+SGt+VY1FJZJRkkFOeg1N1kl2WTXaZZ3VgAR1AL3NPAZ7ZqT3qQ0HBjIKiOjGrThRAMYGpnRlFbY9iMqFiQlXBqSqoqvZJqKBigqpn7WHGedrnYwZKSQaUAPW2llVAUao+XbVn/dNXP4rKaeJKbezTvebnd10/17et9WEv88zmwtAnQVBQEFdddRVXXXWVkd39QnZ2Ng6Hg4QE92/PCQkJ9TYszszMrHO83W4nOzubdu3a1TumoSbIc+fO5amnnqo9R4sJs8UnE/dWgrdtI5TTnlsKFVSblvbzZi/VBKoZs2IlMiiYIEsAgeZAgi3B2sMaTLA5mLCAsOpvtFXPscd+IW7DG8SrClG3rUDxIpUBcOPIjny+LZ0vd5zgsal9vF/x1mmMJp6OeS+ebA6na+WVIfFk0ONJJzq0SkQYicAERWnPLRF5UlXDjYEBIn1tTRMSB7lHDBllplT9vdtFBBnzt9KLxb38dw51p+48IcQaQp+4vvSZ/DK8eSHkb4Nb/wbJ5+NwOsgtzyWrLIvssmzyyvMoqiyqjg5XFFJsK2F3RjYnCgtQTJVEhqiEBUGlsxKb04bNYaPSWVmvdYKKih0VFLAp9X3+Oz38+PPH/UM97dkf1DX5lv489w8Oi2e/J7+stsvPz2fFihWkp6ejKArt2rVj4sSJrsLxpuT0xqaqqjbY7LSu8adv9/aYs2fP5qGHHnL9XFhYSIcOHfhbt4cIDTWyQqWOc3kQhq315aHGNrXGD2rVf64Bqj5C1WpS9J+dDu1LjKp9d1FUp/ZQVEz6NypUTDgxKyomk/a/uknRgkNmiwmzyYTZbMakKNrXL3OAlrIxWcFs1X62BkNAmPZstlb9Bmpfr/43qLA7KC63k1ti42RhOZmF5WQUlJOZX05qbik5JfpNxv0YsaEBdE8Ip0ebCHpGVNKlaBtxJ9djPbEJxVGJCTArZkw9pmAaegu2+P5sOlrAsl2nWLMvh7JKFVAIsFj404Se3H5+Z8zerPrK2AE/3a6JtUn/NHRDGdopmp4J4ew/WcTnW497fENx0WkMbHwTUrxfEXsspwS7UyU0wEzbunrzNYZBjycdvWjcp8hTRaH279rLKIgeeYowEnmylWo1RzXn4QXVkScD7VnApxV3qbl6sbhvPe08XWl3OlMHJNaZuvOIdgNh2G2w+W1Y+gjcvRaz2UJ8SLy7jUcNym0O7v9wG4d3aynmR6f0YtbYLnV+/jtVJw6nA3vxSRw//Av7jv/hUJ2oCjgi2qMOvB5H3ytwBkVoH6c4UVUVJ9pnrIqKqqrun8do95vSSjspOaXkFFeQV2ojr6SS3JIK8stsVNod2B1gczpxOJ3YHdrqU4tZIVixEUYZ4ZQSYnYQarIRbLITZLIThI0As0KAScViBosCVhOYTSZMZjMmxYTZbMJkUjCZLGAyo5gsmEwKiskMihnFZNI+xxVz1eIDE6piQlX0HIJS9ZpaES/ttqJA1dWeLunUuno3NnRTc99Y59/TSPaypKSUq5nV6DifxdP8+fP517/+xdSpU10r637++WeefPJJHnnkEe644w5fT1EncXFxmM3mWhGhU6dO1Yoc6bRt27bO8RaLhdjY2AbH1HdMgMDAwDqbIV864loiIrz/pin4Rk5xBXszitiTUcDuE4XsPlHI4axisiogKxfW7y2rGjkAGEBC4O1cGbqLy2zL6GvbDbuXwO4lbHL2YKl9Ciudw3BiolNsCJcPTOTqoe3p5O3Ko7xj8MmtWn1Wzykw8p5Gd6kLRVG4cVRHnvhiNwt/SeWWMckNCvtadDpPez61G0pzvaqBOXRKS9l1bRPm3Tl19Jong2k7n2p/atYaVRRqKUwv0Iu1jbVmqYo6KWawei9CXOLJqMeVD/3tqovFDay0s1dC5q/aa4PiaUr/tjzz9Z4GU3cNcvEc2P259u9989sw8q56h5ZW2pk5fyNbjuURYDbx3LUDuWxg/XWRJocN0y9vYl377+oFAd0u1WxHul3qc4H34LY+7S4YRCu7aQbx9Oyzz7J161bCwtzD+M888wxDhw5tMvEUEBDA0KFDWbVqlZuNwKpVq7j88svr3Gf06NF89dVXbttWrlzJsGHDsFqtrjGrVq1yq3tauXIlY8aMaYKrEJqC2LBAzu8eyPndq1d0lVTY2ZtRyK/pBfyaXsCRrBKO55WRXVzByYoA3qgYwhsMoZ9yhNsty5lm2sBw0wGGBxwgJ7A9pUPvof24O1ACvLz5qSrsWKR9860sgoj2cPmrPhV0XjE4iblL93HwVDGbUvIY0dmLIuCweK1wN/uA5vfUa6rHu+riqVu8gZQd+Jy2i/LFLNISoAkXW6kmZrwUTz7VPNWsdzLwd/fJqgBq9Lfz3mVc72nXwYhB5qk92peFoEiI6eL9/kC7SGOpOxchMZr57Dd/hO+ehnYDqhZOuON0qjzw4Xa2HMsjIsjCf28exsgu9fSiVFXNwXzlHM09HaDtAJg0V1vRKpwT+CyeFEWhuLi4lngqLi429u3UCx566CFmzpzJsGHDGD16NP/5z39ITU11+TbNnj2b9PR03nvvPQDuueceXnnlFR566CFmzZrFhg0bmD9/vtsquvvvv58LLriAf/3rX1x++eV88cUXfPvtt/z4o29tLYSWJTTQwrDkGIYluwuNcpuD9Pwy0nJLqbA7iQweRXjQzWTZc4jd+z6B294mtvw4sesfh+0vaN8qh93uWfSkNBe+uh/2fqn93GEUXPWmoeXiNYkIsnL5oEQ+3JTGoo2p3okn0FJ32Qe0uicvxNPhLC2F09VIvRP4XDCut2gxlLYD7SauiycvqRZPPkSeDNQ7QXXkqaTSgc3hxOpti5TwqhCGHvnzgoz8cgCSGjN8rYuaKTsf7gU+pe4Aht4Guz7XWhO9dzlcswB6uq8E/9fyfazcc5IAs4m3bx1e63PCReavsHw2pKzTfg5LgEue1FrDGPDQElovPoun//u//+PCCy+kX79+rrTd8ePH2b17N88995zPE2yI6667jpycHJ5++mkyMjLo168fS5cupVMnzak5IyOD1NRqK//OnTuzdOlSHnzwQV599VUSExN56aWXXDYFAGPGjOHDDz/k8ccfZ86cOXTt2pWPPvpIPJ7OUoKsZrrGh9G1VjQlEjo+CRc9DNs+0PyR8lNhzVxY809IGgrdJ0D38dBuUPUHZ2UJFJ6o/pAtzgSTBcbNhvMf9JtXy4yh7flwUxrf7T3p/Q01aRhsWQCZDSwZqgNX2s5o5KkwXXsOb2dod5+ctkETT0UZBsWTD73tfPB4AoiosSigoMxGnLcGi7p4Kqp/0Ut9ZBRoKW5DDYENmGPWhc+pO5MZbvxES5sfXAEf3gjTX4LBNwHw4cZU3lx7BIBnZwyoWziVZMP3z8DW97S6UEsQjP6d9v90oMH/H4RWjWHxtHLlSgYOHMi0adOYPHkyGzdu5MSJE6iqSlJSEiNGjMBsbvpl+vfdd1+9jYgXLFhQa9uFF17I1q1bGzzmjBkzmDFjhj+mJ7R2AkJh5N0w7A7Y+wVseA3SN1c/1vxDS0OFxEHRido35tjucPV/Ddd81MfgjtHEhgZobsZHcxnTzQvTybb9tefMX7UUhAdRAadT5bAvNgWqCgVV4inSWGsYPfLUEv3tfEvbGfd4Aq05dHiQhaJyu0HxVCVWizK82k1VVTIKtMhTu0gDkaeTu7Tn05pde0u7yGCGdopmy7E8Y6k70PreXb8QvvwD7PgffPFbKMnmp4QbeXyJNs/7L+nOFYNP64hReEJLu/84r1oE970Sxj8NUY132xDOXgyLp6uuuoqysjLi4+MZOHAggwYNYvz48Vx66aX+nJ8gnBmYLdDvau1ReAIOfQsHV8LhNVotSc16koAwzYCz+wS46DHtg9vf0zEpXNyrDZ9sOc6qvSe9E0/xvbRoWFmeFg2KbN/oLhmF5ZRWOrCYFGNmieX5mlkiNGpOWh+ugnGjtT8GxZPTqVJc6Y+0nbHIE2jXXlRuNxZ1qxl58lAsA+SV2qiwa8vxEyK9FGxOJ2Qd0F7H9/Zu3zqY0r8dW47lGU/dgbaS94rXtLq/n16Eb5+kiOVcr/Qivvsg/jCmqhaqJBv2fAG7Fle58Vet5Go3UFsl20nqXwUfxFNRURH79+9nx44d7Nixg61bt/LSSy8xatQovv76a0JDDfZBEoQznYhEGHKz9rBXwvFNYC+HiCTtPYO1Ld5yaZ8EPtlynG/3nuSJaX08rzG0BkFcT20FUuavHoknPWWXHBfqfc0NVEedgmMMi8koveappHkjT8WVdtfqaJ8iTz6Ip8hgK2mUGWvRoltDOCo1wexhzZ2esosLCyDQ4mUWoTBdE8smC8QYFDs1qJm6S8kuITnO4P1FUWD805RaYwhZ8yST2MAk6wZIA/59vxZFLs2ttpYArVZx6C0w4DppkSK4MFzhlpmZSa9evbjuuuv4xz/+wfLly0lNTcXhcPDMM8/4c46CcOZiCYDk86DbJdCmV7MJJ4Cx3eMItJhIyy1j/8ki73aumbrzgMO+rrTT650ijTcK1yNPheV2HHV5wjSGQfGkp+wCzCZjRpE+1jxBjXovI0aZlsDqHndepO70YnFDKbus/dpzbDeXd5svtIsM5sIe8agq/PWr3S5/PiNU2B3cvHcE11XM4QPLlVR2mVCdgivJ0oRT4mCY8Dd4cDfcsQIG3SDCSXDDcOQpKSmJuLg4Bg0a5ErbDR48mOeff54pU6bwz3/+05/zFAThNEICLJzfLY7v9p3i2z0n6dXWC+HWtj/s/NDjonG9LUvXNga/8RdUNfGKaDzKVR+RpxVOx4QGNDC6DgyLJx+KxWuez2DNE1QbhBpyVwet7qk0RxNPCX092iWjUBNPbY0Ui2dXiScv+9k1xBOX9WHyvHWs2Z/F8l2ZTO7v/cIDVVX586c72Xwsj/Cg/vxt1t0EJIRrb1YUa/MOjvFLtEw4uzEceTpw4ABvvPEGY8aM4dChQ8yZM4d+/fpx/vnnk5OTw0033cSLL77I6tWr/TlfQRBqcGkfLSWzau8p73b0MvLk8ngyalPgh8iT1WwiPFATMIaKxn2MPPksnnyIPEUE+1jvZWDFXUa+lrZLNCKesvZpz/G9vN+3HrrGh3HPhZpf1FNf7aG4wnvH9Ze+O8SS7ScwmxRev3Eo3XXhBNqquaShIpwEjzAceerWrRvdunVz629XWFjI6tWrufLKK1FVlffff589e/ZQWlrql8kKguDOJb01z6QdafneLePWxVNeimbi2Ei6sTptF97guHrRa54ijIsngMgQK0UVdmMiwsfIU4S3fQR1XCaZPkSefDEIhRriyfO0XWaBHnkykrbTi8V7er9vA9x3UTeWbD9Bam4pL6w6wJxpfTze94vt6bzwrTavv13Rz81EVxC8xXDkKTIykgsvvJD777+fd955hy1btpCRkcHSpUvp2rUrCxcuZPPmzRQVeVmLIQiCx7QJD2JQhygAvvMm+hQSUy1kTu5ucGheSaWrX6DhtJ0r8mQ8bQc+2hUYFE+FZS0feapu0eJD2g68ijydqCoYT4zyMvKkqjUiT/4VT0FWM09frqUdF6xPYfcJz/6WW47l8qdPtBT1XRd04TcjxGZA8A3D4undd9/l4osvJi0tjWeeeYbhw4fTu3dv/ve///Hyyy+7xjWH15MgnMuMr0rdfbvXSwdpD1N3ur9TUlQwIQEGBYSr5sm3yJNf+tsZrXkKNBh58kPBeFQLpO1ckSdvTSlLsjRrChStYNzPjOvZhqn92+Fwqjy+ZBfORhYPfLE9nVvf2USlw8mEPgn8eZL/UonCuYvhtN0VV1zBFVdc4fq5uLiYjIwMkpKSCAnxv6+NIAh1M75PAv9esZ8fD2VTWmn3XOC07Q8HljdaNK7XO3WJNxh1cjr9UvMENewKjIinoCjt2dvIk79qnnwoGI+uKo7PNWrT4KVRZk2DzERvW7PoUafoZLAaSPl5wJxpfViz/xTbUvP5cFMaN4ysHUkqKLPxxBe7+GL7CQBGJMcw7/pBmE1N2zZMODfwWzOesLAwunfvLsJJEJqZ7m3C6BgTQqXdydoD2Z7v6GHkyedi8dJszWMIBcKNGWTquJrktkjBuK81T8YjT/rKQsN9/byMPNU0yGwT4aVBpm5T4OeUXU3aRgbxxwna8Z/6ajd3vruJd9encCSrGFVV+eVIDlNeXMcXVcXhD1zanf/NGmk8cioIpyH/kgShlaMoCpf2TuDtn47y7d6TTOrX1rMddfF0ai84bPX68RzypS0LVKfswhI0XywfiK5K2xmLPFWJl4pCcDo89u3xyarAYat2VveDeMot9jXylKlFAhtpYnsiXzfIDPTeILMZxBPAzaM78d2+k/x0KIdv957i26qav3aRQWQWlqOq0DEmhHnXD2JIx+gmnYtw7iFtoAXhLECve/p+3ynPDSSjkiEgHBwVkH2w3mGunnYtaJCpE6kXjBtabVcjbabXIXmAT1YFFTUWzPiQtoutEk9FFXYq7I5GRtdBaBtA0QwgSxuPTma6etr54vHUtOLJYjbx/u0j+fr35/PnSb0Y0zWWALOJjAJNOF0ztD1L7x8rwkloEiTyJAhnAcOSo4kMtpJbUsm21Ly6O8OfjskEbftB6gatiWtC7WXf5TYHx/O0KERXw5En/9gUQHXkydBqO0sgWILBXqal7oI9u6m6rAoM9bXL156toVp/RINEBFkxmxQcTpW8EhttI72MBpktENYGik9qdU9hbRocrrdmMSSeXJGnpi/MNpkU+iVF0i8pknvHdaW00s7mlDwig60MrFqFKghNgUSeBOEswGo2cVHPeABW7fFi1Z2r7qnuovHDWcWoqrbKLdZbR2+dwqq0nY82BeDjajswVPfkU+TJD/VOoIkE3aYhp6TC2EG8qHvKMBp5KsvTBBpAvP/cxT0lJMDCBT3iRTgJTY6IJ0E4SxjfR7s5eiWeEvppz/UUjR+q0dPO48bDp+PHyFOUK23XfM2BfSoYd3k8+d7zMCa0qt6rxFevp8ZX3LnEk9cr7arMMSOSINCgoaogtAJEPAnCWcIFPeKwmhWOZJe4RE+j1FxxV0ez1cO+rrQDv9Y8ufyOjAoIQ+LJh4JxP3g86ehF480TeTKYtstunmJxQWhpRDwJwllCeJCV0V21lhMeR5/a9AbFXN009jQOZ2krxXwST67Ikz/SdtWF0zaH0/sD+BB5MtSexQ8eTzqxoZplQHN4PVWn7byNPDVPsbggtDQingThLEJfdbdqj4dO0tZgXJ3v60jd6RGsrkZX2jns1Tdrf6y2qyFgDPV581I8OZwqRRUtX/MENewKDIsnzyJPNQ0yvY48NZNNgSC0NCKeBOEsYnxvTTxtS8snq8jD9E49ReN2h5Oj2T5GnoozteXxJovm8+QjZpNCRJWIMVQ07qV4Kq4STmBUPPmv5inalbZr2shTbkkllXYnioLnjaZ1RDwJ5wgingThLKJtZBAD2keiqvCdp73u6nEaT8sro9LhJMhqIsnbwmEdPWUXnuixKWVj6CKiOZoD6/VOARaT92aR4NeaJ321Y56vkafChsWTHnWKCwskwOLFLaKyBApStdfNYFMgCC2JiCdBOMvQo08e1z25xNMut82unnZxYZiM9gNz2RT4nrLTcRWNN0PkyVXv1IJ97XRi/BV5KsnSnM/rwXDKLrtqpV1IHIR44DMmCK0YEU+CcJYxvq8mnvRGwY2ii6fcI26O2LqzuGFzTPCrTYFOdXPg5og8+drXTk/b+S/yZLjmKSROWxyACsWn6h2WaXSlnW5TIFEn4RxAxJMgnGX0TAinQ0wwFZ42Cg6Nq4pKqHByj2vz9tT8quOdGTYFOrpRpm8F4561Z/HJpgD8Kp5iwnwUTyaTR0XjJwyvtNunPbeAOaYgNDcingThLENRFMb39tIw87Si8Qq7g3UHswC4sEfDrTwaRG8K7AebAh3dabs503aGxZM/fZ5qRNw87l94Oi7xVH/dk+G+dtkSeRLOHUQ8CcJZSHWj4JPYPfFDOk08/XIkl5JKB23CA+mb6EO9ThNEnnS7AmNpuyjt2cuC8fBAH9N2fqh50gvlVdVg1A08WnF3Il9L27X1Om1XFXmKk8iTcPYj4kkQzkKGJ0cTFWIlr9TGlmN5je/QdoD2nKGJJ32l3iW92xgvFocmqXlyNQduBp+nQl8jT35M21nNJlfhem4TuoxnFmqRp0RvVljaKyD3qPZaIk/COYCIJ0E4C7GYTVzcU0u3eZS6a1clnk7tQbVX8t0+raD4kl4+eDPZK6CkqjDZD02BdVz97XwpGK8oBGfjETmfCsZVtYZJpu+RJ4DYMM1lPKe4aYwyaxpktvXG4ynnsObnFRhRfQ5BOIsR8SQIZykut/G9J1Hr6FvnRlSyduNzVHJs/zaO55URaDFxXrc44xMoPKE9W4IgJNb4cU5DLxg3VvOkixi1uh6pAfS0XUSwgchTZYkmKMAvkSeojro1VYsWwwaZNXvaGW0gLQitCBFPgnCWMrZHPAFmE8dySjnYWKNgk8mVuju0cz0A53WLIzjAB2NLV7F4ol9vqFG+FIxbAsFSlY7yIHVX6EvkSRdnihmsId7vXwcxen87I1E3aDTyZNggU3raCecYIp4E4SwlLNDCmG5axGfFLg963VWl7ipStwFwcS8fVtlBdbG4H+udoKZJpkEB4UXdk09WBTXrnfwkHl1eT4bTdg1HnnTxlCg97QShQUQ8CcJZzJT+2s1y4S+pVNgdDQ+uijzFl2g3wkt6+yie9MhTZAffjnMaulVBSaWDSrsHKwlPxyvx5IPDuB+bAuvoXk8+u4yX5Wo1aaeRUWBwpd2pvdqzFIsL5wgingThLObyQYm0jQgis7CcT7ccb3hwVeSpt3KMvm3DvDdJPJ0msCkALQqkLwDML2tal/HqyJOBtJ0fmwLr+OwyHhwNZu0YdaXuMowYZNorIeeg9jqhj7F5CUIro9WKp7y8PGbOnElkZCSRkZHMnDmT/Pz8esfbbDb+/Oc/079/f0JDQ0lMTOTmm2/mxIkTbuPGjRuHoihuj+uvv76Jr0YQmoZAi5m7L+wCwOtrDmNryPMprgc2xUq4UsbVnQ36CNWkCWwKAEwmxeX1VNDERpk+mWT60SBTR4+6GRZPitJg3VNGvoHWLLmHwWnXFhz4+W8tCGcqrVY83XDDDWzfvp3ly5ezfPlytm/fzsyZM+sdX1paytatW5kzZw5bt27ls88+48CBA0yfPr3W2FmzZpGRkeF6vPnmm015KYLQpFw/vCNxYQEczytjybb0esdVqmb2OTsCcFG0h87kDeGKPPnPpkCnur9dc4knI5GnfO3ZDwaZOj63aIEG655ckSdvPJ5OVbX0ie8lK+2EcwaDzm8ty969e1m+fDk///wzI0eOBOC///0vo0ePZv/+/fTsWbtoMTIyklWrVrlte/nllxkxYgSpqal07NjRtT0kJIS2bcWrRDg7CA4wM2tsF+Yu28draw5z1ZD2mOswvtx4NJdURyf6Ww6TXHHQ9xO7Vtv5PxpRbVfQdGk7h1OluMKHyJOr5inK+33rwee0HTQceTLSmkWvd2rT2/icBKGV0SojTxs2bCAyMtIlnABGjRpFZGQk69ev9/g4BQUFKIpCVFSU2/aFCxcSFxdH3759efjhhykqKqr7AFVUVFRQWFjo9hCEM4kbR3UiKsTK0ewSvt55os4x3+07yW41GQClqk2LYSpLqiMvfq55gpor7pou8qQLJ/B1tZ0fI081xFOj3l31UU/kSVVVY33tXOJJ6p2Ec4dWKZ4yMzNp06b2SqA2bdqQmenBkmygvLycv/zlL9xwww1ERFR/uN14440sWrSINWvWMGfOHBYvXsxVV13V4LHmzp3rqr2KjIykQwf/ri4SBF8JC7Rwx3mdAXh19SGcpzWWVVWV7/aeYrczWduQuVNzyDaKXu8UEO7Xmh8dV3PgJiwYL6xq/xJoMRFoMeB31QQ1T7p4qnQ43cSdV9QTecopqaTSYcAgU0/bSeRJOIc4o8TTX//611rF2qc/Nm/eDGid409HVdU6t5+OzWbj+uuvx+l08tprr7m9N2vWLC699FL69evH9ddfz6effsq3337L1q1b6z3e7NmzKSgocD3S0tK8vHJBaHpuHpNMeKCFAyeLWbnH/cZ56FQxqbmlHDF1QlVMUJLVYP+zRinUbQqapoA4MkRvDtx0kSe9+a6eIvQaPzYF1gkJsBBk1T62/e0yrked4sMCsZo9vDVUllb3tJPIk3AOcUbVPP3ud79rdGVbcnIyO3fu5OTJ2gWtWVlZJCQ03IvLZrNx7bXXcvToUb7//nu3qFNdDBkyBKvVysGDBxkyZEidYwIDAwkMDGzwOILQ0kQGW7n1vGRe/v4QL39/iPO7x7P+UDZrDmSxuqqX3eCuiShlPSBrnxZ9imhn7GRNWO8ENSJPzSGeggO8Pwc0ic8TQGxoIOn5ZeSWVNIpNtT7A9QTeTphZKVd9n5AhZA4CIv3fi6C0Eo5o8RTXFwccXGN99IaPXo0BQUFbNy4kREjRgDwyy+/UFBQwJgxY+rdTxdOBw8eZPXq1cTGNt5va/fu3dhsNtq1M3gTEYQziNvO68z8H4+y+0QhA59aiaNG+i7QYuLm0Z1g70BNPGXshB4TjZ2ooGk8nnT0aFBBE6btdGGm2yJ4TRPUPIGWutPFkyFckSd38ZRZaMDjSYrFhXOUMypt5ym9e/dm0qRJzJo1i59//pmff/6ZWbNmMW3aNLeVdr169eLzzz8HwG63M2PGDDZv3szChQtxOBxkZmaSmZlJZaX2IXT48GGefvppNm/eTEpKCkuXLuWaa65h8ODBnHfeeS1yrYLgT2JCA7hlTDKgrSbrGBPCzaM78fatw9j2xHgu6Z3gchonY7vxExU2jbu4ji5o8kqMRJ6itOfGxFOVMIs0mrZrgponqK57Mu4yXhV5qijQCvurOJGviSev3MVd9U6SshPOLc6oyJM3LFy4kD/84Q9MmDABgOnTp/PKK6+4jdm/fz8FBdoH5PHjx/nyyy8BGDRokNu41atXM27cOAICAvjuu+948cUXKS4upkOHDkydOpUnn3wSs9mHBqmCcAbx0PgeDO4QRbc2YXSOC61dJ1jlNI4vK+5yjmjPTSSeqgvGmyNtd+bUPIH7ijtDBEZojYptpVr0KbYrUJ22S4zyRjzt057bSFsW4dyi1YqnmJgYPvjggwbH1FzKm5yc3OjS3g4dOvDDDz/4ZX6CcKZiNZuY0LcBH7O2/bXn/FQoy9NaeniDw14dtUocZGSKjeIXn6eKQnA6wVR3AL7A57Rd00ae8nx1Gc89Uqd4SooK8fxYYlMgnKO0yrSdIAhNSHA0RFWZxmb+6v3+2fu1qEZAGMT18O/cqvBLwTiqlrqqB/3YhlbbOWxgKzntfP7B57Qd1LniLl0XT9Ee1jyVF1SnZ6UhsHCOIeJJEITatBuoPWcYSN2lb9GeEweDqWnS3XodUpnNQbnN4d3OlgCwVq1SK8uvd1h1zZOB1XYVNYx1/Zy2awqXcZvDycmqgvEkT1uz6Cm7iCQIjjI+F0FohYh4EgShNm118bTD+3118ZRUt7WHPwgPtLhazBQYqXvSb/ZlefUO8anmSXdXt4aC2b/VEdH+jDxVWUpkFpTjVCHAYnKJs0YRc0zhHEbEkyAItfGlaNwlnob6bz6noSiKS9TkGal70uu4GhBPPlkVNJFNAdSMPFUYP4ieZqsSQK6UXVQwpjr6HtaJ2BQI5zAingRBqI1uV5B9QHOR9hRbGZysikg0oXiC6giMofSVB+LJJ4dxXTx5W2zvAdUF4wYibjoJfbXnk7tAVUnPqxZPHiM2BcI5jIgnQRBqE94WQuNBdVbfJD0hYyeoDghLaDJ3cZ2YEB9EhJ6209NrdeCTw7guyppAPMWGat0MiivsVNi9rPfSie8FiglKc6D4pFvkyWMk8iScw4h4EgShNopSo2h8u+f71UzZedBn0heiQ7WIUG4TpO0q7A5KKzVhYiht14TiKSK4ut7LcNF4QAjEaBYFnNzlijwleiqeirOgNBtQIK5no8MF4WxDxJMgCHWjp92OeOF91gzF4joxVREYQ35HLvGUX+fbetRJUSA8yEDBty6edDdzP6IoisuqIafYh6JxV+puNycKvLQpyKqKOkUna0JMEM4xRDwJglA3el+7Q9+BrdyzfZqhWFwnRo88GRFPuqipJ/JU0yDT4wLqmrgiT1He7+sBfrEraNtPez652/uaJzHHFM5xRDwJglA37QZDWFvN7DHlx8bHl+ZC3lHtdeLgpp0b1UaZTbHazufWLE2YtoMaReNGrl0nQRNP6sld3tc8iU2BcI4j4kkQhLoxmaDnJO31/qWNj0/fqj3Hdmsy0VATn3q8NSKefLIpgOp0YFOJpzA/pu2yDuC0V6IoXjQFlmJx4RxHxJMgCPXTc6r2vH8ZNNIbsjlTdtC0VgV6w2FD7uLQ9OIpxA9pu8gOEBiB4rTRVTlBQngQARYPbgmqKmk74ZxHxJMgCPXT+QKwhkDRicbdxl1tWZq+WBxqWhU0XcH4mZ6288llXFFc0adeSqrnxeKF6VpTZZNFizIKwjmIiCdBEOrHGgRdL9Ze719W/zhVbfbIkytt52vNUx0RtYKqYxpP2zWteIoN80E41qSq7qmXKdVzmwI96hTbXesTKAjnICKeBEFomJ5TtOeG6p7yUzXfH5MF2vZvlmnp4qnc5qSs0kuzSH0VnKNCc0U/jXxf3MWhyVfb+VTvVZOqyFNvJVWKxQXBC0Q8CYLQMD0mAorW566qkWwtTlQViyf006JVzUBIgNlVo+N19CkgTBN6UGfdk08F47YysFcJsiZP2/nQ3w5ckafeJi/Sdpm7tGcRT8I5jIgnQRAaJjQOOozUXteXumvmlB1oZpGuwmlvV50pSoNF49V97Yy0ZsmvOocZAv3fGBj8GHmqEkBtlHw6B3nQw9DphCNrtNf6vwlBOAcR8SQIQuP0nKw91yueqiJPzSieoMaKOz97PblW2/nUmiWqyVrU6OIpv8yGw9nIKsiGCAwjlQQAOtlTGh///+3deXRTZf4G8CdN0nRPWwLdgYpQEApWGJYqI8qqLGdcKAhTfiLUFbQz4MI4ozAijJ1BR2VcD6ICggcUHY9YFhlQlCIFq4AMItCBli4CbbqnbXJ/f9zclLRJk5u0aZM8n3NyKDf33ryZe0aevsv3Lf0RqC0Xe+56j3H9c4m8HMMTETkmzXs69xXQUGX9nrEZuPi9+LOHw5NUZdytFXc2NgeWJoy7NOdJul8n1rqSCoQKAlDpRqHMGkMzfjL2BgD0qv/F8QWnd4t/XjOOk8XJrzE8EZFjuv7iRrKmJuDMXuv3Lp0CmuqAwHDxPA+S9rfr6FpPbpUq6OSVdgCgVgZYesXcGbq7WFmPkyYxPGkun3R8wS/m8HTtBJc/k8gXMDwRkWMKhf2hO0t9p+uBAKVHmxVt7hlyaZsSO/vbmUyCJTy5N2zXuVXWO6LWU3FFPf4riOEJZcfbP7nuClB0WPy5/0SXP5PIFzA8EZFzBpqrjZ/eKf5DeuITYPtDwO5nxeMeHrIDWuY8uRQg7PQ8VRuaIU0jinAnPEnhrJN0xKTxosp6nJTCU/l/xSFYe87sBQSTWFVcm+jyZxL5AlVXN4CIvETiSCA4Gqi/Avy9n/gPqSQ4Chh8h8ebZNkgtwPDk95cpiBYrUSQ2oWeNC/qebpYWY8LQk80BgQj0FgPXP4F6DXQ9sm/7BH/5JAdEXueiMhJShUwaLr4s2ASK0yPWQT832fA0tPisJ2HRbmzx5u98NRhBTI7Nzz1cCc4mhVX1ENAACrCzNus2Bu6M5lawhOH7IjY80REMkx6Duh3CxA7FOjRr6tb09Lz5Fapgkqrw5X13XtrFklHDNsVV4rFPBt6XAdUHQPKTgCpd7c9saQAqP1VXBSQNNrlzyPyFex5IiLnBWnF4bluEJyAqwNEk/yL7fQ8uVVdHGgJYx4KT5dqXK8yXlwhhqeAWLHSOMpO2D5R6nW65maWKCACwxMRebGre54EGxv8tstOz5O3DNslmrdTuXDFicrgNjQZTSirbgAAhPUeJh60F55O7xL/5JAdEQCGJyLyYlLAMZoEVNW3s1LMFmnTXjtznrr7sF2fHqEAgMLLroWnUn0DBAEIVAVA28ccnqqKxJWUV6u7AhTliz9fy/BEBDA8EZEX06iUCNOIUzdlb9EihZvGasDYMuxXaaku7uLwlGXYLtK1653Up0cIADHsuVJlvMg8ZJcQGYyAkEhAK5Us+Mn6xDN7AQhAr8GANsGNFhP5DoYnIvJqUaEuVtoO0rb8fNXQnVtznozNgEEv/tzJPU8hgSrERIgV1s9dqpV9vTRZPCFSHP6DNO8p/x3rLXgsQ3YsUUAkYXgiIq8WHeLikv0AZUuAump/O7fmPDXoW37u5CKZQMvQ3f9cGLq72Do8SXW6jn8E/GukWATVZLyqRMEkd5tL5DO8NjxVVFQgMzMTWq0WWq0WmZmZqKysbPeae++9FwqFwuo1erT1sluDwYDFixdDp9MhNDQUM2bMQFFRUSd+EyJyh1RlXPawHWBzxV1lR2zNookQ62J1smRzeHKp58k8bBcvhaehGcDvPwKi+gLVJcDW/wPWTQTqLovfJ2lURzWbyOt5bXiaM2cOCgoKkJubi9zcXBQUFCAzM9PhdVOmTEFJSYnltWPHDqv3s7OzsX37dmzZsgUHDhxATU0Npk2bBqPR2FlfhYjc4Fa9IxvhSaowHhnswpwnqQerk+c7SfroxHlP/7vsxrCdedUeALF6+MN5wG+fAALULfsWXnMzoHRxAj2RD/LKIpknT55Ebm4u8vLyMGqU+NvQ22+/jTFjxuDUqVNISUmxe61Go0FsbKzN9/R6PdatW4cNGzZgwgRxfH/jxo1ISkrCnj17MHny5I7/MkTkFpeH7QCbmwO7NWznoZV2kmQ3Vty1mfMkUQcDtz4t9kR9/keg8AAw/F53m0rkU7yy5+ngwYPQarWW4AQAo0ePhlarxbffftvutfv27UOvXr0wYMAAZGVloby83PLekSNH0NTUhEmTWsb24+PjMWTIkHbvazAYUFVVZfUiIs+I6uCeJ7cqjHs4PLWUK5DX8yQIgiU8JUYF2z5J11/ceufpMu5nR9SKV4an0tJS9OrVq83xXr16obS01O51t912GzZt2oS9e/dizZo1OHz4MG699VYYDAbLfQMDAxEVZf0fvpiYmHbvu3r1asvcK61Wi6SkJBe/GRHJ1TFbtIihp6HJiIYmccNjrTs9Tx6YLA60lCuorJNXruBSTSMam01QKICYiKD2T2ZFcaI2ulV4Wr58eZsJ3a1f+flisTaFQtHmekEQbB6XzJo1C1OnTsWQIUMwffp0fPHFF/j555/x+eeft9suR/ddtmwZ9Hq95XXhwgUnvzERuasjNweWhuyUAQqEa1yY1eDhnqdQjQq9wsVyBXJW3Em9TjHhQQhUdat/Boi8Qrea87Ro0SLMnj273XP69u2LH3/8EWVlZW3e+/XXXxETE+P058XFxaFPnz44ffo0ACA2NhaNjY2oqKiw6n0qLy9Henq63ftoNBpoNBqnP5eIOk5Lz5M7+9tVArCuLt7eL0x2eTg8AUDfHqEorzag8HIthiVFOnWNtNIuwd6QHRG1q1uFJ51OB51O5/C8MWPGQK/X47vvvsPIkSMBAIcOHYJer2835LR2+fJlXLhwAXFxcQCA4cOHQ61WY/fu3cjIyAAAlJSU4Pjx48jJyXHhGxFRZ5PC02VXNsht1fPk/qbAXRCedCH4rvAKCi853/Mk1XiKbz1ZnIic4pX9tYMGDcKUKVOQlZWFvLw85OXlISsrC9OmTbNaaTdw4EBs374dAFBTU4OlS5fi4MGDKCwsxL59+zB9+nTodDrccYdYHE6r1WLBggVYsmQJvvzyS3z//ff4/e9/j9TUVMvqOyLqXqTwVNXQjCajSd7Frfa3k+YNuR6eKs339Vx4cmXS+FlzXagk9jwRuaRb9TzJsWnTJjz66KOWlXEzZszA2rVrrc45deoU9Hqx4q9SqcSxY8fw/vvvo7KyEnFxcbjlllvw4YcfIjw83HLNSy+9BJVKhYyMDNTX12P8+PF49913oVQqPffliMhp4hAbIAhiz1HPcBlD6HbmPLlUpuCq+3h62A6QF56OFVcCAIYkaNs/kYhs8trwFB0djY0bN7Z7jiAIlp+Dg4Oxc+dOh/cNCgrCq6++ildffdXtNhJR51MGKBAZrEZFXRMq6ho7JDy5P2wX6dr1LuhrKZTp3LCdodmIU6XVAIBUhicil3jlsB0R0dVcrvUkhaeGSsBkssx5ivSiOU/SsN2V2kZL+GvPqdJqNBkFRIWo7dd4IqJ2MTwRkddzucq4VI9JMAGN1S0FMkNcqG0kCF0SnsI0KktvmzPbtPxYJE5lSE2MdG1FIRExPBGR97OsuJMbntRBgFoc9kJ9BfT1zQBcHLYzVAOCeQ9MD4YnAOhrLpbpzDYtx8zhaSiH7IhcxvBERF7PUuvJzf3tpNV2Lg3bSb1OqiBxfzgPsqy4u+REz1OxGJ44WZzIdQxPROT1LHOe3Nyixa3Vdg2V1vfzoGSdcyvuGpqM+LlMnCw+NJHhichVDE9E5PVcnvMEdFx46oL5ThJpjztHPU8/lVTBaBKgCwtEnNbBnnZEZBfDExF5vZaeJ1e2aIkU/6yvcK/CuIc3Bb6aVOvJUbmC4+Yhu9QELSeLE7mB4YmIvF50qBh2rtS6vkWLqa4SVQ1SeHJhtV036Hm6XNto+Q62XL3Sjohcx/BERF4vOlRcql9R6/rmwI01lyHV1XWr56kLwlN4kBq6MDHw/a+dPe640o6oYzA8EZHXk+Y8yS6SCVjCTnPNZQBASKASgSoX/tPYBdXFr+Zom5a6xmacLjdXFudkcSK3MDwRkdeLMg/b1TcZUd9olHexOewYa8Xw403Vxa/WxzLvyXZ4+uliFUwC0Ctcg5gIThYncgfDExF5vTCNCmqlOAG6Qm65AnPYEczhx6Xq4gBQX2l1P09LNu9xd87OsJ0034klCojcx/BERF5PoVAgytWhO3PYCWhwt+ep0up+nuao5+mYZaVdpKeaROSzGJ6IyCdEu7k5sKpRDBcuTRYHuv2cJyk8seeJyH0MT0TkE6SeJ1eH7QKbqgC4WCAT6Po5T+Zhu0s1jahuVa6gxtCMM7/WAOC2LEQdgeGJiHxCdJibPU8mAzRohNZLw1NEkBo9zL1vrYtlnijWQxCAeG0QeoZruqJ5RD6F4YmIfILLW7QEhgEKJQAgEjWuDds11QPN9eLPXRSeAKCvnT3ujnEzYKIOxfBERD7B5c2BFQpL4IlU1CDSperileZ7KQFNhPzrO4i9Pe640o6oYzE8EZFPiA6RtmhxvVBmJGpdm/PUUGm+T6QYxrpIv55hAIA395/FB4fOQzCXTLestOO2LEQdguGJiHxClKur7YBWPU/etTXL1X4/qg+uT4pEtaEZf9p+DHPePoTjxXqcM/dEpXLYjqhDMDwRkU+QShW4s79dhKIWEe6Ep6BI+dd2IG2IGh89lI6/TLsOwWolDp69jBlrDwAAEqOCLf8bEZF7GJ6IyCdEuzrnCYBgrs0UiRrXhu26Sc8TACgDFFhwUzJ2Zv8W6f16wGTe7JjznYg6DsMTEfmElp6nRstcH2cZA8VgEalwcbVdNwpPkt49QrBp4Sj87c5UDEuKxNxRfbq6SUQ+Q9XVDSAi6ghSkcxmk4BqQzMigpwPQdUB4YgC0COgDmEaF/6z2A3DEyBuWzN7ZG/MHtm7q5tC5FPY80REPiFIrURIoFiv6VK1Qda1V0xifaS4wHooXFkt103DExF1DoYnIvIZ8ZHBAIDiynpZ15U3idfpVHUOzrSjizcFJiLPYngiIp+RFCWGoAtX5IWniwbxukiF7U11HWLPE5FfYXgiIp/RO1qssH2hQl4P0vkGcb+3cKHGtQ+2hKdI164nIq/C8EREPiPJHJ7OX5EXns7ViJPEg5urXPtg9jwR+RWGJyLyGYlRYngqkhmeTleJK/PUzTVAswsVyjnnicivMDwRkc9IijbPeapwfs5Tk9GEn6tVMAjm0gbVJfI+1NgMGMS94xieiPwDwxMR+Qxp2O5KbSNqDc1OXVOqb4BRCEAJeogHqorlfWiDvuXnLt6ehYg8w2vDU0VFBTIzM6HVaqHVapGZmYnKysp2r1EoFDZff//73y3njBs3rs37s2fP7uRvQ0QdISJIbdlexdlJ49J5Faqe4gF9kbwPbagU/9REAErWHSbyB14bnubMmYOCggLk5uYiNzcXBQUFyMzMbPeakpISq9c777wDhUKBu+66y+q8rKwsq/PefPPNzvwqRNSBkszzns5fdi48FZuH+Go0seIB/QV5HygN84Xq5F1HRF7LK39NOnnyJHJzc5GXl4dRo0YBAN5++22MGTMGp06dQkpKis3rYmNjrf7+6aef4pZbbsE111xjdTwkJKTNuUTkHZKig3GsWO/0vKci83mNYfFAHeT3PFWaw5Y2Sd51ROS1vLLn6eDBg9BqtZbgBACjR4+GVqvFt99+69Q9ysrK8Pnnn2PBggVt3tu0aRN0Oh0GDx6MpUuXorq6ut17GQwGVFVVWb2IqGtIPU8XnFxxJ1UjV0jhR254knqqIhmeiPyFV/Y8lZaWolevXm2O9+rVC6WlpU7d47333kN4eDjuvPNOq+Nz585FcnIyYmNjcfz4cSxbtgw//PADdu/ebfdeq1evxooVK+R9CSLqFNKk8SIn5zxJ52l0fYDTcKHn6X/in5F95F1HRF6rW/U8LV++3O6kbumVn58PADY37xQEwelNPd955x3MnTsXQUFBVsezsrIwYcIEDBkyBLNnz8a2bduwZ88eHD161O69li1bBr1eb3lduCBzzgQRdRgpPDm7RYvU8xQR01c8oJe52o7DdkR+p1v1PC1atMjhyra+ffvixx9/RFlZWZv3fv31V8TExDj8nK+//hqnTp3Chx9+6PDcG264AWq1GqdPn8YNN9xg8xyNRgONRuPwXkTU+Sz721XUOfyFymgSUFLZAADomWCe+2jQi+UHgrTOfSCH7Yj8TrcKTzqdDjqd4xUrY8aMgV6vx3fffYeRI0cCAA4dOgS9Xo/09HSH169btw7Dhw/HsGHDHJ574sQJNDU1IS4uzvEXIKIulxAVDIUCqGs04nJtI3Rh9n+xKatqQLNJgCpAgZ49eohFLusrxN4nZ8KTydQyzBfZu4O+ARF1d91q2M5ZgwYNwpQpU5CVlYW8vDzk5eUhKysL06ZNs1ppN3DgQGzfvt3q2qqqKmzduhULFy5sc98zZ87gr3/9K/Lz81FYWIgdO3Zg5syZSEtLw4033tjp34uI3KdRKRETLg7HO5o0Lq20i48MhjJAAWgTxTecnfdUUwYYGwGFEgiPd7nNRORdvDI8AeKKuNTUVEyaNAmTJk3C0KFDsWHDBqtzTp06Bb1eb3Vsy5YtEAQB99xzT5t7BgYG4ssvv8TkyZORkpKCRx99FJMmTcKePXugVCo79fsQUcfpLc17clCuoLhSDFcJkeJQn2XekrO1nqTzIuJZIJPIj3jt/9ujo6OxcePGds8RBKHNsfvvvx/333+/zfOTkpKwf//+DmkfEXWdxOhgfFfoRM+TeVJ5YpQUnsw9T85u0VJ53nwd5zsR+ROv7XkiIrJHqvXkqFyBtNIuQQpPEQnin84O20nhifOdiPwKwxMR+RypXMF5J+c8JZrDluw5T1xpR+SXGJ6IyOdYyhU4qPVk6Xlydc4TazwR+SWGJyLyOb17iD1JFyvrYTS1nfsIACaTYNkUuO2cp4uAyej4g9jzROSXGJ6IyOfEhAchUBmAZpOAEr3t3qdLNQY0Gk0IUACxWvNOA+GxYtkBU7NYhqA9gnDVnCduzULkTxieiMjnBAQoLJPA7Q3dSWUM4rTBUCvN/ykMUIplBwDH27TUXQGazHOqpInmROQXGJ6IyCclWsKT7UnjbeY7SSyTxh3Me9Kbe53CYgB1UPvnEpFPYXgiIp/UUijTdniSyhhY5jtJnF1xxzIFRH6L4YmIfJJUrsBuz1NFqxpPEqfDE1faEfkrhici8klSoUx7W7QUtV5pJ3E2PHGlHZHfYngiIp+UFO3snKcQ6zeknqQq9jwRkW0MT0Tkk6Sep/JqAxqarGs2CYJgf86Ts1u0sEwBkd9ieCIinxQZoka4Rtz7vPUed1dqG9HQZAIAxEW2WiknDdvVXQYa29neRVptx2E7Ir/D8EREPkmhUCDRMmncet6TNN8pJkIDjUppfWGQFggMF3+uslPrqUEvvgAO2xH5IYYnIvJZlj3uWvU82a3xBAAKheNaT9J8p+AoQBPWIW0lIu/B8EREPsteuYKW+U4hba4B4HjFnWWlHWs8Efkjhici8lm9HQzbtanxJNFKk8btDNtxpR2RX2N4IiKfJZUrON+q56nYXo0nicOeJ1YXJ/JnDE9E5LNaCmXWoayqwVKywNLzZGvOE9DSo2R3zhPDE5E/U3V1A4iIOos0p6m6oRmjVn0JANCoAtBoNFm934ajnicO2xH5NfY8EZHPCg5UInN0H0SFqBGgEI8Zmk0QBEAXFmgZ1mtDCk9VxYAgtH2fW7MQ+TX2PBGRT3vud0Pw3O+GQBAE1BiaUVnXBH19ExKjgtvWeJKExwNQAM0NYrHMUF3Le031QO2v4s/seSLySwxPROQXFAoFwoPUCA9Sw2HkUQUCYTFATanYy3R1eJKG7ALDxTpPROR3OGxHRGSLvXlPV2/LolB4tk1E1C0wPBER2WIvPHGyOJHfY3giIrLFbnjihsBE/o7hiYjIFnu1nrg1C5HfY3giIrLF3hYtHLYj8nsMT0REtkjDdpd+Bo681zJ8x54nIr/HUgVERLZE9wNUQYChCvjsUfGYLgWouij+zPBE5LfY80REZEtQBPDAV8C4ZUDibwBFAHDpFAABUIcCoT27uoVE1EXY80REZE/PFGDcU+Kr7gpwbj9Q+A3QezRrPBH5Ma/teXr++eeRnp6OkJAQREZGOnWNIAhYvnw54uPjERwcjHHjxuHEiRNW5xgMBixevBg6nQ6hoaGYMWMGiorsbA5KRP4jJBoYfAcw9R9A6t1d3Roi6kJeG54aGxsxc+ZMPPTQQ05fk5OTgxdffBFr167F4cOHERsbi4kTJ6K6utpyTnZ2NrZv344tW7bgwIEDqKmpwbRp02A0GjvjaxAREZGXUQiCrS3Dvce7776L7OxsVFZWtnueIAiIj49HdnY2nnzySQBiL1NMTAxeeOEFPPDAA9Dr9ejZsyc2bNiAWbNmAQAuXryIpKQk7NixA5MnT3aqTVVVVdBqtdDr9YiIiHDr+xEREZFnOPvvt9f2PMl17tw5lJaWYtKkSZZjGo0GN998M7799lsAwJEjR9DU1GR1Tnx8PIYMGWI5xxaDwYCqqiqrFxEREfkmvwlPpaWlAICYmBir4zExMZb3SktLERgYiKioKLvn2LJ69WpotVrLKymJxfOIiIh8VbcKT8uXL4dCoWj3lZ+f79ZnKFqtkBEEoc2x1hyds2zZMuj1esvrwoULds8lIiIi79atShUsWrQIs2fPbvecvn37unTv2NhYAGLvUlxcnOV4eXm5pTcqNjYWjY2NqKiosOp9Ki8vR3p6ut17azQaaDQal9pFRERE3qVbhSedTgedTtcp905OTkZsbCx2796NtLQ0AOKKvf379+OFF14AAAwfPhxqtRq7d+9GRkYGAKCkpATHjx9HTk5Op7SLiIiIvEu3Ck9ynD9/HleuXMH58+dhNBpRUFAAALj22msRFhYGABg4cCBWr16NO+64AwqFAtnZ2Vi1ahX69++P/v37Y9WqVQgJCcGcOXMAAFqtFgsWLMCSJUvQo0cPREdHY+nSpUhNTcWECRO66qsSERFRN+K14emZZ57Be++9Z/m71Jv0n//8B+PGjQMAnDp1Cnq93nLOE088gfr6ejz88MOoqKjAqFGjsGvXLoSHh1vOeemll6BSqZCRkYH6+nqMHz8e7777LpRKpWe+GBEREXVrXl/nqTtinSciIiLvwzpPRERERJ2A4YmIiIhIBoYnIiIiIhm8dsJ4dyZNI+M2LURERN5D+nfb0XRwhqdOUF1dDQDcpoWIiMgLVVdXQ6vV2n2fq+06gclkwsWLFxEeHu5w65furKqqCklJSbhw4QJXDXYxPovug8+i++Cz6D585VkIgoDq6mrEx8cjIMD+zCb2PHWCgIAAJCYmdnUzOkxERIRX/5/Bl/BZdB98Ft0Hn0X34QvPor0eJwknjBMRERHJwPBEREREJAPDE9ml0Wjw7LPPQqPRdHVT/B6fRffBZ9F98Fl0H/72LDhhnIiIiEgG9jwRERERycDwRERERCQDwxMRERGRDAxPRERERDIwPBERERHJwPBEWL16NRQKBbKzs9s9z2Aw4Omnn0afPn2g0WjQr18/vPPOO55ppJ9w9lls2rQJw4YNQ0hICOLi4jB//nxcvnzZM430YcuXL4dCobB6xcbGtnvN/v37MXz4cAQFBeGaa67BG2+84aHW+ja5z+Ljjz/GxIkT0bNnT0RERGDMmDHYuXOnB1vsu1z5/4Xkm2++gUqlwvXXX9+5jfQwbs/i5w4fPoy33noLQ4cOdXhuRkYGysrKsG7dOlx77bUoLy9Hc3OzB1rpH5x9FgcOHMC8efPw0ksvYfr06SguLsaDDz6IhQsXYvv27R5qre8aPHgw9uzZY/m7Uqm0e+65c+dw++23IysrCxs3bsQ333yDhx9+GD179sRdd93lieb6NDnP4quvvsLEiROxatUqREZGYv369Zg+fToOHTqEtLQ0TzTXp8l5FhK9Xo958+Zh/PjxKCsr68zmeRzDkx+rqanB3Llz8fbbb2PlypXtnpubm4v9+/fj7NmziI6OBgD07dvXA630D3KeRV5eHvr27YtHH30UAJCcnIwHHngAOTk5nmiqz1OpVE7/Vv3GG2+gd+/e+Oc//wkAGDRoEPLz8/GPf/yD4akDyHkW0jOQrFq1Cp9++ik+++wzhqcOIOdZSB544AHMmTMHSqUSn3zySec0rItw2M6PPfLII5g6dSomTJjg8Nx///vfGDFiBHJycpCQkIABAwZg6dKlqK+v90BLfZ+cZ5Geno6ioiLs2LEDgiCgrKwM27Ztw9SpUz3QUt93+vRpxMfHIzk5GbNnz8bZs2ftnnvw4EFMmjTJ6tjkyZORn5+Ppqamzm6qz5PzLFozmUyorq62/LJH7pH7LNavX48zZ87g2Wef9VALPYs9T35qy5YtOHr0KA4fPuzU+WfPnsWBAwcQFBSE7du349KlS3j44Ydx5coVzntyk9xnkZ6ejk2bNmHWrFloaGhAc3MzZsyYgVdffbWTW+r7Ro0ahffffx8DBgxAWVkZVq5cifT0dJw4cQI9evRoc35paSliYmKsjsXExKC5uRmXLl1CXFycp5ruc+Q+i9bWrFmD2tpaZGRkeKC1vk3uszh9+jSeeuopfP3111CpfDRmCOR3zp8/L/Tq1UsoKCiwHLv55puFxx57zO41EydOFIKCgoTKykrLsY8++khQKBRCXV1dZzbXp7nyLE6cOCHExcUJOTk5wg8//CDk5uYKqampwn333eeBFvuXmpoaISYmRlizZo3N9/v37y+sWrXK6tiBAwcEAEJJSYknmug3HD2Lq33wwQdCSEiIsHv3bg+0zP+09yyam5uFESNGCK+//rrl2LPPPisMGzbMgy3sfD4aCak9R44cQXl5OYYPH245ZjQa8dVXX2Ht2rUwGAxtJgPGxcUhISEBWq3WcmzQoEEQBAFFRUXo37+/x9rvS1x5FqtXr8aNN96Ixx9/HAAwdOhQhIaGYuzYsVi5ciV7OzpQaGgoUlNTcfr0aZvvx8bGorS01OpYeXk5VCqVU70j5DxHz0Ly4YcfYsGCBdi6datTw+AkX3vPorq6Gvn5+fj++++xaNEiAOIQqiAIUKlU2LVrF2699VZPN7nDMTz5ofHjx+PYsWNWx+bPn4+BAwfiySeftLmK4sYbb8TWrVtRU1ODsLAwAMDPP/+MgIAAJCYmeqTdvsiVZ1FXV9emK1w6T+A+3x3KYDDg5MmTGDt2rM33x4wZg88++8zq2K5duzBixAio1WpPNNFvOHoWALB582bcd9992Lx5M+cAdqL2nkVERESb/6a99tpr2Lt3L7Zt24bk5GRPNbNzdXHPF3UTrYeKnnrqKSEzM9Py9+rqaiExMVG4++67hRMnTgj79+8X+vfvLyxcuLALWuvbHD2L9evXCyqVSnjttdeEM2fOCAcOHBBGjBghjBw5sgta61uWLFki7Nu3Tzh79qyQl5cnTJs2TQgPDxcKCwsFQWj7LM6ePSuEhIQIf/jDH4SffvpJWLdunaBWq4Vt27Z11VfwGXKfxQcffCCoVCrhX//6l1BSUmJ5XT3VgFwj91m05ovDdlxtRzaVlJTg/Pnzlr+HhYVh9+7dqKysxIgRIzB37lxMnz4dr7zyShe20j+0fhb33nsvXnzxRaxduxZDhgzBzJkzkZKSgo8//rgLW+kbioqKcM899yAlJQV33nknAgMDkZeXhz59+gBo+yySk5OxY8cO7Nu3D9dffz2ee+45vPLKKyxT0AHkPos333wTzc3NeOSRRxAXF2d5PfbYY131FXyG3GfhDxSCwH5+IiIiImex54mIiIhIBoYnIiIiIhkYnoiIiIhkYHgiIiIikoHhiYiIiEgGhiciIiIiGRieiIiIiGRgeCIiIqIu89VXX2H69OmIj4+HQqHAJ5980qmfV11djezsbPTp0wfBwcFIT0/H4cOHZd2D4YmIqB3jxo2DQqGAQqFAQUGBW/e69957Lffq7H8giLxFbW0thg0bhrVr13rk8xYuXIjdu3djw4YNOHbsGCZNmoQJEyaguLjY6XswPBEROZCVlYWSkhIMGTLErfu8/PLLKCkp6aBWEfmG2267DStXrsSdd95p8/3GxkY88cQTSEhIQGhoKEaNGoV9+/a59Fn19fX46KOPkJOTg9/+9re49tprsXz5ciQnJ+P11193+j4qx6cQEfm3kJAQxMbGun0frVYLrVbbAS0i8h/z589HYWEhtmzZgvj4eGzfvh1TpkzBsWPH0L9/f1n3am5uhtFoRFBQkNXx4OBgHDhwwOn7sOeJiPzK5s2bERQUZNVFv3DhQgwdOhR6vd7p+4wbNw6LFy9GdnY2oqKiEBMTg7feegu1tbWYP38+wsPD0a9fP3zxxRed8TWI/MKZM2ewefNmbN26FWPHjkW/fv2wdOlS3HTTTVi/fr3s+4WHh2PMmDF47rnncPHiRRiNRmzcuBGHDh2S1SvM8EREfmX27NlISUnB6tWrAQArVqzAzp078cUXX8juFXrvvfeg0+nw3XffYfHixXjooYcwc+ZMpKen4+jRo5g8eTIyMzNRV1fXGV+FyOcdPXoUgiBgwIABCAsLs7z279+PM2fOAAAKCwstcwntvRYtWmS554YNGyAIAhISEqDRaPDKK69gzpw5UCqVTreLw3ZE5FcUCgWef/553H333YiPj8fLL7+Mr7/+GgkJCbLvNWzYMPz5z38GACxbtgx/+9vfoNPpkJWVBQB45pln8Prrr+PHH3/E6NGjO/R7EPkDk8kEpVKJI0eOtAk3YWFhAICEhAScPHmy3ftERUVZfu7Xrx/279+P2tpaVFVVIS4uDrNmzUJycrLT7WJ4IiK/M23aNFx33XVYsWIFdu3ahcGDB7t0n6FDh1p+ViqV6NGjB1JTUy3HYmJiAADl5eXuNZjIT6WlpcFoNKK8vBxjx461eY5arcbAgQNl3zs0NBShoaGoqKjAzp07kZOT4/S1DE9E5Hd27tyJ//73vzAajZaA4wq1Wm31d4VCYXVMoVAAEH97JiLbampq8Msvv1j+fu7cORQUFCA6OhoDBgzA3LlzMW/ePKxZswZpaWm4dOkS9u7di9TUVNx+++2yP2/nzp0QBAEpKSn45Zdf8PjjjyMlJQXz5893+h6c80REfuXo0aOYOXMm3nzzTUyePBl/+ctfurpJRH4tPz8faWlpSEtLAwD88Y9/RFpaGp555hkAwPr16zFv3jwsWbIEKSkpmDFjBg4dOoSkpCSXPk+v1+ORRx7BwIEDMW/ePNx0003YtWtXm1+G2sOeJyLyG4WFhZg6dSqeeuopZGZm4rrrrsNvfvMbHDlyBMOHD+/q5hH5pXHjxkEQBLvvq9VqrFixAitWrOiQz8vIyEBGRoZb92DPExH5hStXruC2227DjBkz8Kc//QkAMHz4cEyfPh1PP/10F7eOiLwJe56IyC9ER0fbXJHz6aefunQ/WxWOCwsL2xxr7zdqIvJO7HkiInLgtddeQ1hYGI4dO+bWfR588EHL8moi8l4Kgb8WERHZVVxcjPr6egBA7969ERgY6PK9ysvLUVVVBQCIi4tDaGhoh7SRiDyL4YmIiIhIBg7bEREREcnA8EREREQkA8MTERERkQwMT0REREQyMDwRERERycDwRERERCQDwxMRERGRDAxPRERERDIwPBERERHJwPBEREREJMP/A5UcT3jg2XO2AAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "L = 1e-8 # m\n", "x0 = L / 2.\n", "sig = 1e-10 # m\n", "kappa = 5e10 # m^-1\n", "\n", "N = 1000\n", "dx = L / N\n", "\n", "def psi0(x):\n", " return np.exp(-(x-x0)**2/(2*sig**2))*np.exp(1j*kappa*x)\n", "\n", "psi = np.zeros([N+1],dtype=np.cdouble)\n", "for k in range(N+1):\n", " x = dx * k\n", " #print(x,\" \",x0,\" \", psi0(x))\n", " psi[k] = psi0(x)\n", "psi[0] = 0\n", "psi[N] = 0\n", "\n", "norm0 = integral_psi2(psi, dx)\n", "\n", "import matplotlib.pyplot as plt\n", "plt.title(\"Free particle in a box\")\n", "plt.xlabel('${x}$ [m]')\n", "plt.ylabel('${\\psi_0(x)}$')\n", "plt.xlim(L/2 - 0.05*L,L/2 + 0.05*L)\n", "plt.plot([dx*k for k in range(N+1)], np.real(psi), label=\"Re ${\\psi_0(x)}$\")\n", "plt.plot([dx*k for k in range(N+1)], np.imag(psi), label=\"Im ${\\psi_0(x)}$\")\n", "plt.plot([dx*k for k in range(N+1)], np.abs(psi)**2, label=\"$|{\\psi_0(x)|^2}$\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now integrate over time" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.display import clear_output\n", "import time\n", "\n", "current_time = 0.\n", "h = 1e-19\n", "nsteps = 100\n", "for i in range(500):\n", " psi = schrodinger_finitediff_solve(psi, h, nsteps, dx, me, 2)\n", " current_time += h * nsteps\n", " \n", " clear_output(wait=True)\n", " plt.title(\"Wave equation at t = \" + '{:.1f}'.format(current_time*1.e18) + \" as\")\n", " plt.xlabel('${x}$ [m]')\n", " plt.ylabel('${\\psi_0(x)}$')\n", " plt.xlim(0,L)\n", " plt.ylim(-1,1)\n", " # plt.xlim(L/2 - 0.05*L,L/2 + 0.05*L)\n", " #plt.plot([a*k for k in range(N+1)], np.real(psi), label=\"Re ${\\psi_0(x)}$\")\n", " #plt.plot([a*k for k in range(N+1)], np.imag(psi), label=\"Im ${\\psi_0(x)}$\")\n", " plt.plot([a*k for k in range(N+1)], np.abs(psi)**2, label=\"${|\\psi_0(x)}|^2$, norm = \" + '{:.5f}'.format(integral_psi2(psi,dx)/norm0))\n", " plt.legend()\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python [conda env:CompPhys]", "language": "python", "name": "conda-env-CompPhys-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 4 }