{
"cells": [
{
"cell_type": "markdown",
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"source": [
"## Perturbation Theory: Energy Shifts and Perturbed Wavefunctions \n",
"\n",
"#### Advanced Quantum Physics content\n",
"\n",
"In this exercise we will be investigating first order perturbation theory on a harmonic potential and a square well. Detailed below are the results derived within the AQP course which we shall be using.\n",
"\n",
"Total Hamiltonian:\n",
"\\begin{equation}\n",
" \\hat{H} = \\hat{H}^{(0)}+\\hat{H}'\n",
"\\end{equation}\n",
"\n",
"First order energy shift:\n",
"\\begin{equation}\n",
" \\Delta E_n^{(1)} = \\langle n^{(0)} | \\hat{H}' | n^{(0)} \\rangle\n",
"\\end{equation}\n",
"\n",
"First order perturbed wavefunctions:\n",
"\\begin{equation}\n",
" |n^{(1)}\\rangle \\approx | n^{(0)} \\rangle + \\sum_{m \\neq n} | m^{(0)} \\rangle \\frac{\\langle m^{(0)} | \\hat{H}' | n^{(0)} \\rangle}{E_n^{(0)}-E_m^{0}}\n",
"\\end{equation}\n",
"\n",
"In the following we are working in units where $\\hbar = 1$\n",
"\n",
"Importing libraries which we will be using in this exercise, pycav.quantum contains functions specifically designed for this program. The following will outline the basic use of this program so that it can be used with ease in the exercise at the end."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np\n",
"from scipy.special import hermite\n",
"from scipy.misc import factorial\n",
"from scipy.integrate import quad\n",
"\n",
"import matplotlib.pyplot as plt\n",
"\n",
"import pycav.quantum as pm\n",
"\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Define a potential for use in plotting. The function should take an array argument, params, containing the necessary parameters which define the potential. The function should then return a function of position, x.\n",
"\n",
"E.g. Harmonic potential: params[0] is the mass and params[1] is the angular frequency $V(x) = \\frac{1}{2} m \\omega^2 x^2$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def harmonic_potential(params):\n",
" def V(x):\n",
" return 0.5*params[0]*params[1]**2*x**2\n",
" return V"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Define the form of the unperturbed wavefunctions. The function should take the params argument as well as the primary quantum number, n. The function should then return the wavefunction as a function of position, like with the potential. The harmonic oscillator wavefunctions are of the form given here\n",
"\n",
"Also define the form of the unperturbed energies. The function just needs to return the value of the energy of state $n$ by using the params array."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def harmonic_unperturb_wf(params,n):\n",
" alpha = params[0]*params[1]\n",
" def psi_n(x):\n",
" n_fact = factorial(n)\n",
" y = np.sqrt(alpha)*x\n",
" n_herm = hermite(n)\n",
" return (alpha/np.pi)**(0.25)*(1./(2**n*n_fact)**0.5*n_herm(y)*np.exp(-y**2/2.))\n",
" return psi_n\n",
" \n",
"def harmonic_unperturb_erg(params,n):\n",
" return (n+0.5)*params[1]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With these functions in place we can plot the unperturbed system. This is done by the plot_levels function in the perturb_module. It will plot the first 4 wavefunctions, with their origins placed at their energy level. The function requires the arguments: unperturb_wf, unperturb_erg, potential and params with an additional optional arguments, x_lims which takes a list with the $x$ axis limits e.g. x_lims = [-0.1,0.1] and plot_zoom which takes a list which contains one element which is the factor by which wavefunctions are multiplied on the plot so they are visible."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
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julZnGhqwvqICmysrUd7SgjGtYXKYry88LWRRhVGScLC+Hl9XVeGrqipU6/W4LygIkzt3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\njMGCBQtExyEtJUkSDl84jEVHF0G3gy5WjlqJUX24DpFo9erVOHToEH7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evFh0HCIhWHSJ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\nrkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"h_params = [0.5,2000.]\n",
"pm.plot_levels(harmonic_unperturb_wf,harmonic_unperturb_erg,harmonic_potential,\n",
" h_params,x_lims = [-0.1,0.1], plot_zoom = [200])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now it is time to define the perturbing potential $\\hat{H}'$. This is simply a function of $x$ which returns the potential value at $x$. If statements can be used to define potentials which have different behaviour in different regions. "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def perturbation(x):\n",
" return 1000.*x**4"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First order energy shifts and perturbed wavefunctions for individual levels can be called via first_order_energy_sft and first_order_wf respectively. These return the energy shift as a float and perturbed wavefunction as a function of position. The first argument for both is the principle quantum number of the energy level in question. For first_order_energy_sft a list of principle quantum numbers can also be passed and a list of energy shifts will be output. The mandatory arguments are familiar. \n",
"\n",
"There are the additional optional arguments limits and tolerance. limits puts the limits on the expectation value and overlap integrals done for the first order energy shift and perturbed wavefunction calculations respectively. Tolerance sets the level at which additional terms in the perturbed wavefunction sum are discarded. If the fraction accompanying $|m^{(0)}\\rangle$ is less than the tolerance the sum is truncated."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"dE_0 = pm.first_order_energy_sft(0,perturbation,harmonic_unperturb_wf,h_params,limits = [-np.inf,np.inf])\n",
"\n",
"perturb_1 = pm.first_order_wf(1,perturbation,harmonic_unperturb_wf,harmonic_unperturb_erg,\n",
" h_params,tolerance = 0.01,limits = [-np.inf,np.inf])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Performs a similar plot to plot_levels with the unperturbed wavefunctions with faint lines and the perturbed wavefunctions with solid lines. The perturbed wavefunctions origin is also shifted by the first order energy shift.\n",
"\n",
"plot_perturb has the optional arguments x_lims, tolerance, limits and plot_zoom. The first 3 have the usual meaning given above. plot_zoom is a list with 2 element, the first of which scales the size of the wavefunction on the plot (default value is 200). The second element scales the factor by which the first order energy shift is increased so that it can be viewed on the plot (default value is 100)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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r67mkrEyulT2AdcEgN7e10ZdK8f36ei4c5di2RHZkWHMiwRlFReOy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\nRERklBh0iYiIiMgo/T90n0SMuUFkigAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.plot_perturb(perturbation,harmonic_unperturb_wf,harmonic_unperturb_erg,harmonic_potential,\n",
" h_params,tolerance = 0.01,plot_zoom = [200,10000])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercises\n",
"\n",
"1. For the harmonic potential, investigate linear and quadratic perturbations and higher order $x^n$. What do you notice about the first order energy shift as a function of $(n+1/2)$?\n",
"(Theoretical Exercise: Why do the shifts have the shown function form? Hint: use ladder operators)\n",
"\n",
"2. For a square well with infintely high walls, write down the unperturbed wavefunctions and the unperturbed energies and create the required functions\n",
"\n",
"3. Investigate a small step in potential near the centre of the well such that perturbation has the form:\n",
"\\begin{align}\n",
" V'(x) &= \\epsilon \\ \\mbox{for} \\ |x| < b/2\n",
"\\end{align}\n",
"where $b \\ll a$ where $a$ is the width of the well. Give the first order energy shift to the ground state and first excited state\n",
"\n",
"4. Investigate a linear perturbation, $V'(x) \\propto -x$, and give the first order energy shift to the ground state and first excited state. Now write a function to calculate the second order energy shift:\n",
"\\begin{equation}\n",
" \\Delta E_n^{(2)} = \\sum_{m \\neq n} \\frac{\\langle m^{(0)} | \\hat{H}' | n^{(0)} \\rangle}{E_n^{(0)}-E_m^{0}}\n",
"\\end{equation}\n",
"Use [SciPy Quad](http://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.quad.html) to calculate the matrix elements. You should truncate the sum when the terms become negligibly small. Why should you perform seperate sums for even and odd $m$? Find the second order energy shift for the ground and first excited states.\n",
"\n",
"5. Use the optional argument return_list = True in first_order_wf to return a tuple containing (perturbed_wf, k_list, I_list). k_list, I_list contain a list of the principle quantum numbers and prefactors in the sum of the unperturbed states respectively. i.e.\n",
"\\begin{equation}\n",
" |n^{(1)}\\rangle \\approx |n^{(0)}\\rangle + \\sum_{k \\in k_{list}} I_{list}[k] \\ |k^{(0)}\\rangle\n",
"\\end{equation}\n",
"Use this to show the linear combination of states which creates the perturbed state (increasing the perturbation size makes this clearer). Also plot the perturbed wavefunction for the ground state, what is the interpretation of this?\n",
"\n",
"6. With the system in the ground state of the perturbed system ($V'(x) \\propto -x$), write down the time dependence once the perturbation is switched off (only consider the above expansion to first order in the sum). \n",
"\n",
"7. (Extra) Plot this evolution."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution\n",
"\n",
"#### Harmonic Potential:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0.0, 0.0, 0.0]\n",
"[0.0, 0.0, 0.0]\n"
]
}
],
"source": [
"def perturbation(x):\n",
" return 1000.*x\n",
"\n",
"dE = pm.first_order_energy_sft([0,1,2],perturbation,harmonic_unperturb_wf,h_params,limits = [-np.inf,np.inf])\n",
"print(dE)\n",
"\n",
"def perturbation(x):\n",
" return 1000.*x**3\n",
"\n",
"dE = pm.first_order_energy_sft([0,1,2],perturbation,harmonic_unperturb_wf,h_params,limits = [-np.inf,np.inf])\n",
"print(dE)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"All odd powers show vanishing first order energy shifts"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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LGpP5b0mS2s8mXNKozH9Lkjru7/4O9tgDjj666kpK5RKFkkbk+t+SpFIceijsv3/VVZTO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\nzlHPqqgAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def perturbation(x):\n",
" return 1000.*x**2\n",
"\n",
"dE = pm.first_order_energy_sft([0,1,2,3,4],perturbation,harmonic_unperturb_wf,\n",
" h_params,limits = [-np.inf,np.inf])\n",
"\n",
"fig1 = plt.figure(figsize = (12,12))\n",
"ax1 = plt.subplot(221)\n",
"ax1.plot([0.5,1.5,2.5,3.5,4.5],dE,'b-')\n",
"\n",
"def perturbation(x):\n",
" return 1000.*x**4\n",
"\n",
"dE = pm.first_order_energy_sft([0,1,2,3,4],perturbation,harmonic_unperturb_wf,\n",
" h_params,limits = [-np.inf,np.inf])\n",
"\n",
"ax2 = plt.subplot(222)\n",
"p = np.polyfit([0.5,1.5,2.5,3.5,4.5],dE,2)\n",
"ax2.plot([0.5,1.5,2.5,3.5,4.5],dE,'bx')\n",
"n = np.linspace(0.5,4.5,100)\n",
"ax2.plot(n,p[0]*n**2+p[2],'r-.')\n",
"\n",
"def perturbation(x):\n",
" return 1000.*x**6\n",
"\n",
"dE = pm.first_order_energy_sft([0,1,2,3,4],perturbation,harmonic_unperturb_wf,\n",
" h_params,limits = [-np.inf,np.inf])\n",
"\n",
"ax2 = plt.subplot(223)\n",
"p = np.polyfit([0.5,1.5,2.5,3.5,4.5],dE,3)\n",
"ax2.plot([0.5,1.5,2.5,3.5,4.5],dE,'bx')\n",
"n = np.linspace(0.5,4.5,100)\n",
"ax2.plot(n,p[0]*n**3+p[2]*n,'r-.')\n",
"\n",
"def perturbation(x):\n",
" return 1000.*x**8\n",
"\n",
"dE = pm.first_order_energy_sft([0,1,2,3,4],perturbation,harmonic_unperturb_wf,\n",
" h_params,limits = [-np.inf,np.inf])\n",
"\n",
"ax2 = plt.subplot(224)\n",
"p = np.polyfit([0.5,1.5,2.5,3.5,4.5],dE,4)\n",
"ax2.plot([0.5,1.5,2.5,3.5,4.5],dE,'bx')\n",
"n = np.linspace(0.5,4.5,100)\n",
"ax2.plot(n,p[0]*n**4+p[2]*n**2+p[4],'r-.')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"All even powers, $x^{2n}$, show polynomial dependence $\\Delta E = a_n (n+1/2)^{n} + a_{n-2} (n+1/2)^{n-2} + ...$ down to either constant or linear term\n",
"\n",
"#### Square Well:\n",
"\n",
"Only parameters needed in params is well width, $a$, and particle mass, $m$."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def square_unperturb_wf(params,n):\n",
" a = params[0]\n",
" m = n+1\n",
" def psi_n(x):\n",
" return np.sqrt(2./a)*np.sin((m*np.pi/a)*(x+a/2.))\n",
" return psi_n\n",
" \n",
"def square_unperturb_erg(params,n):\n",
" m = n+1\n",
" return (m**2*np.pi**2)/(2*params[1]*params[0]**2)\n",
"\n",
"def square_potential(params):\n",
" def V(x):\n",
" return 0.0*x\n",
" return V"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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DlSxLL8bjejgc1m9HR/VgV5e+392tDYz4YxEpWpaeHh7WD/v7dWB8XN8MBvWtUIjH8OID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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sq_params = [0.2,2.]\n",
"pm.plot_levels(square_unperturb_wf,square_unperturb_erg,square_potential,sq_params,plot_zoom = [25])"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0.00019999151727509405, 5.442104613134156e-09]\n"
]
}
],
"source": [
"def perturbation(x):\n",
" if np.abs(x) < 0.001:\n",
" return 0.01\n",
" else:\n",
" return 0.\n",
"\n",
"dE = pm.first_order_energy_sft([0,1],perturbation,square_unperturb_wf,sq_params,\n",
" limits = [-sq_params[0]/2.,sq_params[0]/2.])\n",
"print(dE)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Perturbation theory results suggest $\\Delta E^{(1)}_1 \\approx \\frac{2\\epsilon b}{a}$ and $\\Delta E^{(1)}_2 \\approx 0$. In this case $\\frac{2\\epsilon b}{a} = 0.0002$ for $\\epsilon = 0.001$, $b = 0.002$ and $a = 0.2$"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[-1.3997512624623706e-15, -2.6857882711871884e-15]\n"
]
}
],
"source": [
"def perturbation(x):\n",
" return 1000.*x\n",
"\n",
"dE = pm.first_order_energy_sft([0,1],perturbation,square_unperturb_wf,sq_params,\n",
" limits = [-sq_params[0]/2.,sq_params[0]/2.])\n",
"print(dE)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Both first order energy shifts are, of order, $0$, leading contribution from second order energy shift"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def second_order_energy_sft(n,H,unperturb_wf,unperturb_erg,params,tolerance = 0.01,\n",
" limits = [-np.inf,np.inf]):\n",
" \n",
" def combine_functions(i,j):\n",
" def integrand(x):\n",
" psi_i = unperturb_wf(params,i)\n",
" psi_j = unperturb_wf(params,j)\n",
" return H(x)*psi_i(x)*psi_j(x)\n",
" return integrand\n",
" \n",
" def E_diff(i,j):\n",
" E_i = unperturb_erg(params,i)\n",
" E_j = unperturb_erg(params,j)\n",
" return E_i-E_j\n",
"\n",
" def find_k_values(even,k_list,I_list):\n",
" truncate = False\n",
" if even:\n",
" k = 0\n",
" else:\n",
" k = 1\n",
" while not truncate:\n",
" if n != k:\n",
" I, I_err = quad(combine_functions(n,k),limits[0],limits[1])\n",
" E_nk = E_diff(n,k)\n",
" \n",
" if abs(I/E_nk) < tolerance:\n",
" truncate = True\n",
" else:\n",
" I_list.append(I/E_nk)\n",
" k_list.append(k)\n",
" k += 2\n",
" else:\n",
" k += 2\n",
" return k_list,I_list\n",
" \n",
" k_list = []\n",
" I_list = []\n",
" \n",
" k_list,I_list = find_k_values(True,k_list,I_list)\n",
" k_list,I_list = find_k_values(False,k_list,I_list)\n",
" \n",
" return sum(I_list)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"61.685027506808474 246.7401100272339\n",
"0.19778821633439841 -0.06568724606206797\n"
]
}
],
"source": [
"dE_0 = second_order_energy_sft(0,perturbation,square_unperturb_wf,square_unperturb_erg,sq_params,\n",
" tolerance = 0.001,limits = [-sq_params[0]/2.,sq_params[0]/2.])\n",
"dE_1 = second_order_energy_sft(1,perturbation,square_unperturb_wf,square_unperturb_erg,sq_params,\n",
" tolerance = 0.001,limits = [-sq_params[0]/2.,sq_params[0]/2.])\n",
"\n",
"print(square_unperturb_erg(sq_params,0),square_unperturb_erg(sq_params,1))\n",
"print(dE_0,dE_1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"At second order, an energy shift is seen for both the ground and first excited states (although with opposite sign)."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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jgaVLuUhvwACgXTtddItYgYKxyDkYBuscp00DFi5k7WygKirigroVK4DwcKB/f3WZEP/7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\nYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n = 0\n",
"\n",
"perturb_n, k_list, I_list = pm.first_order_wf(n,perturbation,square_unperturb_wf,square_unperturb_erg,\n",
" sq_params, tolerance = 0.1,\n",
" limits = [-sq_params[0]/2.,sq_params[0]/2.],\n",
" return_list = True)\n",
"\n",
"\n",
"k_list.append(n)\n",
"I_list.append(1.)\n",
"\n",
"fig2 = plt.figure(figsize = (12,6))\n",
"ax = plt.subplot(111)\n",
"x = np.linspace(-0.1,0.1,200)\n",
"\n",
"ax.plot(x,perturb_n(x),'b')\n",
"\n",
"V = square_potential(sq_params)\n",
"perturb_h = np.array([perturbation(y) for y in x])*0.005\n",
"\n",
"for k in k_list:\n",
" unperturb_k = square_unperturb_wf(sq_params,k)\n",
" if k != n:\n",
" ax.plot(x,I_list[k_list.index(k)]*unperturb_k(x),'r',alpha = 0.5)\n",
" else:\n",
" ax.plot(x,unperturb_k(x),'b',alpha = 0.5)\n",
"\n",
"ax.plot(x,V(x)+perturb_h,'k')\n",
"ax.set_xlim((np.min(x),np.max(x)))\n",
"ax.set_yticks([])"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"The time dependence of the above state is given by:\n",
"\\begin{equation}\n",
" |\\psi(t)\\rangle = |1^{(0)}\\rangle e^{-iE_1 t} + c_{21} |2^{(0)} \\rangle e^{-iE_2 t}\n",
"\\end{equation}"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import pycav.display as display\n",
"import matplotlib.animation as anim\n",
"\n",
"N = 200\n",
"\n",
"def psi_t(i):\n",
" t = i*0.0005\n",
" sum_I = np.sum(I_list)\n",
" for k in k_list:\n",
" unperturb_k = square_unperturb_wf(sq_params,k)\n",
" psi_r[:,i] += (I_list[k_list.index(k)]*unperturb_k(x)*np.cos(square_unperturb_erg(sq_params,k)*t)\n",
" /(sum_I*np.max(unperturb_k(x))))\n",
" psi_i[:,i] += (I_list[k_list.index(k)]*unperturb_k(x)*np.sin(square_unperturb_erg(sq_params,k)*t)\n",
" /(sum_I*np.max(unperturb_k(x))))\n",
" psi_a[:,i] += psi_r[:,i]**2+psi_i[:,i]**2\n",
"\n",
"\n",
"psi_r = np.zeros((x.shape[0],N))\n",
"psi_i = np.zeros((x.shape[0],N))\n",
"psi_a = np.zeros((x.shape[0],N))\n",
"\n",
"for j in range(N):\n",
" psi_t(j)\n",
"\n",
"def nextframe(arg):\n",
" line_r.set_data(x,psi_r[:,arg])\n",
" line_i.set_data(x,psi_i[:,arg])\n",
" line_a.set_data(x,psi_a[:,arg])\n",
" \n",
"fig3 = plt.figure(figsize = (12,9))\n",
"ax1 = plt.subplot(211)\n",
"ax2 = plt.subplot(212)\n",
"ax1.set_xlim([np.min(x),np.max(x)])\n",
"ax1.set_ylim([-1.0,1.0])\n",
"ax2.set_xlim([np.min(x),np.max(x)])\n",
"ax2.set_ylim([0.0,1.])\n",
"line_r = ax1.plot(x,np.zeros_like(x),'b')[0]\n",
"line_i = ax1.plot(x,np.zeros_like(x),'r')[0]\n",
"line_a = ax2.plot(x,np.zeros_like(x),'k')[0]\n",
"animate1 = anim.FuncAnimation(fig3, nextframe, frames = N)\n",
"animate1 = display.create_animation(animate1, temp = True)\n",
"display.display_animation(animate1)"
]
},
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