{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Schroedinger Equation for Hydrogen Atom\n", "\n", "\n", "The Schroedinger equation is:\n", "\n", "\\begin{eqnarray}\n", "(-\\frac{\\hbar^2}{2m}\\nabla^2-\\frac{Z e^2}{4\\pi\\varepsilon_0 r})\\psi(\\vec{r})=E \\psi(\\vec{r})\n", "\\end{eqnarray}\n", "\n", "using ansatz:\n", "\n", "$\\psi(\\vec{r}) = Y_{lm}(\\hat{r})\\; u(r)/r$\n", "\n", "and introducing dimensionless variables:\n", "\n", "\\begin{eqnarray}\n", "x = \\frac{r}{r_B}\\\\\n", "\\varepsilon = \\frac{E}{E_0}\n", "\\end{eqnarray}\n", "where\n", "\\begin{eqnarray}\n", "&& r_B = \\frac{4\\pi\\varepsilon_0 \\hbar^2}{m e^2} \\approx 0.529 A\\\\\n", "&& E_0 = \\frac{\\hbar^2}{2 m r_B^2} == Ry \\approx 13.6 eV\n", "\\end{eqnarray}\n", "\n", "we get the differential equation\n", "\n", "\\begin{eqnarray}\n", "u''(x)-\n", "\\left(\\frac{l(l+1)}{x^2}-\\frac{2Z}{x}-\\varepsilon\\right)u(x)=0\n", "\\end{eqnarray}\n", "\n", "Next we rewrite into the system of first order equations:\n", "\n", "\\begin{eqnarray}\n", "y = \\left(u(x),u'(x)\\right)\\\\\n", "\\frac{dy}{dx} = \\left(u'(x),u''(x)\\right)\n", "\\end{eqnarray}\n", "\n", "with boundary conditions\n", "\\begin{eqnarray}\n", "&&u(0) = 0 \\rightarrow \\psi(0)<\\infty\\\\\n", "&&u(\\infty)=0 \\rightarrow \\int |\\psi(r)|^2 r^2 dr \\propto \\int u^2(r)dr < \\infty\n", "\\end{eqnarray}\n", "\n", "Because boundary conditions are given at the two ends, we need so-called shooting method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Shooting algorithm:**\n", "\n", "Suppose the two boundary condistions are given at $a$ and $b$, i.e., $u(a)=u(b)=0$. Then\n", "\n", "* Choose $u(a)=0$ and $u'(a)=c$, with $c$ some constant.\n", "* Solve for $u(x)$ to the other end, and check if $u(b)=0$.\n", "* Using root finding routine find energy $\\varepsilon$ for which u(b)=0. This is the bound state.\n", "* Continue with increasing energy $\\varepsilon$ until sufficient number of bound states is found" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Some remarks**\n", "\n", "* It turns out that forward integration of the radial Sch. Eq. is unstable. It is better to start integrating from infinity, and then continue down to zero.\n", "* It is better to use logarithmic mesh for radial variable rather than linear. Radial functions need smaller number of points in logarithmic mesh" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**The implementation will follow these steps**\n", "\n", "
    \n", "
  1. call SciPy routine 
    integrate.odeint
    to integrate the one-electron Schroedinger equation. Note that the distance is measured in units of bohr radius and energy units is Rydberg ($1 Ry = 13.6058...eV$)\n", "
    2. \n", "

    \n", "

  2. The boundary conditions are $u(0)=0$ and $u(\\infty)=0$. \n", "\n", "Use shooting method to obtain wave functions:\n", "
      \n", "
    1. Use logarithmic mesh of radial points for integration. Start integrating\n", " from a large distance ($R_{max} \\sim 100$). At $R_{max}$ choose\n", " $u=0$ and some nonzero (not too large) derivative.
      2. \n", "
    2. Integrate the Schroedinger equation down to $r=0$. If\n", " your choice for the energy $\\varepsilon$ corresponds to the bound state, the wave function at $u(r=0)$ will be zero.
      3. \n", "
    \n", "\n", "

    \n", "

  3. Start searching for the first bound state at sufficiently negative energy (for example $\\sim -1.2 Z^2$) and increase energy in sufficiently small steps to bracket all necessary bound states. Ones the wave function at $r=0$ changes sign, use root finding routine, for example 
    optimize.brentq,
    to compute zero to very high precision. Store the index and the energy of the bound state for further processing.
    4. \n", "\n", "
  4. Ones bound state energies are found, recompute $u(r)$ for all bound states. Normalize $u(r)$ and plot them.
    5. \n", "\n", "
  5. Compute electron density for various atoms (for example He, Li, ..) neglecting Coulomb repulsion:\n", "

    \n", " Populate first $Z$ lowest laying electron states and\n", " compute \n", " $\\rho = \\sum_{lm\\in occupied} u_{lm}^2(r)/(4\\pi r^2)$. \n", " Each state with quantum number $l$ can take $2(2l+1)$\n", " electrons. Be carefull, if atom is not one of the Nobel gases\n", " (He, Ne, ...) the last orbital is only partially filled.\n", "\n", "

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall: \n", "\n", "\\begin{eqnarray}\n", "&& y = (u(r), u'(r) )\\\\\n", "&& dy/dr = (u'(r), u''(r))\n", "\\end{eqnarray}\n", "\n", "\\begin{eqnarray}\n", "u''(r)=\n", "\\left(\\frac{l(l+1)}{r^2}-\\frac{2Z}{r}-\\varepsilon\\right)u(r)\n", "\\end{eqnarray}" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [], "source": [ "from scipy import *\n", "from numpy import *\n", "from scipy import integrate\n", "from scipy import optimize\n", "from numba import jit # This is the new line with numba\n", "\n", "@jit(nopython=True)\n", "def Schroed_deriv(y,r,l,En):\n", " \"Given y=[u,u'] returns dy/dr=[u',u''] \"\n", " (u,up) = y\n", " return array([up, (l*(l+1)/r**2-2/r-En)*u])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we try linear mesh and forward integration. It is supposed to be unstable.\n", "We know the ground state has energy $E_0=-1 Ry$ and we should get $1s$ state with integrating Scroedinger equation. " ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [], "source": [ "R = linspace(1e-10,20,500)\n", "l=0\n", "E0=-1.0\n", "\n", "ur = integrate.odeint(Schroed_deriv, [0.0, 1.0], R, args=(l,E0))" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from pylab import *\n", "%matplotlib inline\n", "\n", "plot(R,ur[:,0],label='odeint')\n", "plot(R,R*exp(-R),label='exact') # expected solution u = r * exp(-r)\n", "legend(loc='best')\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recal `Euler's method` and `Runge Kutta` method" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import Image\n", "Image('https://upload.wikimedia.org/wikipedia/commons/thumb/1/10/Euler_method.svg/2560px-Euler_method.svg.png')\n" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Image('https://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Runge-Kutta_slopes.svg/1920px-Runge-Kutta_slopes.svg.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indeed the integration is unstable, and needs to be done in opposite direction. Let's try from large R." ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [], "source": [ "R = linspace(1e-10,20,500)\n", "l=0\n", "E0=-1.0\n", "Rb=R[::-1] # invert the mesh\n", "\n", "urb = integrate.odeint(Schroed_deriv, [0.0, -1e-7], Rb, args=(l,E0))\n", "ur = urb[:,0][::-1] # we take u(r) and invert it in R.\n", "\n", "norm=integrate.simps(ur**2,x=R)\n", "ur *= 1./sqrt(norm)" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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INoMZEwdw02k9aahGslQTKzthyL94PB4XExPj6zJE/MoP2/YRtSCOxMwDjBvQiYcnDyakTVNflyV+wszWOec8Vd2OPtEs4ucO5Bfx1LIk3vl2K51bNuHl60ZwwaDO+gCa1AiFgoifcs6xJHYHD38Yz+6DBdx0Wk/uPb8/LRrr11Zqjp5dIn4obW8uDyyKY2XSLgaHtOLVGz0MDW3j67IkACgURPxIUUkpr321hWc/3UiQGQ9MGsgNY3qokSy1RqEg4ifWbd3H9AWxbNiRw/kDO/PQxYPopkay1DKFgoiPZecV8eSyDby7ZhtdWjVh7vUjOH9QF1+XJQFKoSDiI845otdnMjM6gT0HC7jl9F788bx+aiSLT+nZJ+ID2/bkMmNRHF9s3MWQkNa8cdOpDA5p7euyRBQKIrWpqKSUf36ZwnOfbiI4qAEPXTSQ68f0JKiBPnMg/kGhIFJL1m3dS9T8OJJ25jB+UBcevHggXVurkSz+RaEgUsOyc4t4/OMN/Ou7bYS0acqrN3gYN7Czr8sSqZRCQaSGOOdY/NN2HolOYF9uEbef0Yu7x/WjuRrJ4sf07BSpAVv3HGLGwji+3LSbYd3b8NYtgxnUTY1k8X8KBZFqVFhc1kh+fkVZI3nm5EFcO6qHGslSZygURKrJ2tS9RM2PZVPWQSYM6cKDFw2ic6smvi5L5IQoFESqaH9uIY8v3cC8tWmEtGnK6zd5ODdCjWSpmxQKIifJOceiH8sayfvzirjjzN7cNS6cZo30ayV1l569Iidhy+5D3L8wjq+SdzO8exvemTKEgd1a+boskSpTKIicgILiEuZ+nsILK5Np3LABj1wymGtGhqmRLPWGQkHES2tS9jB9YRzJWQeZNLQrD0waSCc1kqWeUSiIHMe+Q4U8tjSR92PSCW3blDduPpVz+nfydVkiNUKhIHIUzjnmf5/B7CWJHMgrYtpZfbhrbDhNGwX5ujSRGqNQEKlEyq6DzFgYx+rNe4gMa8Ojlw4hoosayVL/KRREKigoLmHOqs28tHIzjYMbMHvKYK4+NYwGaiRLgFAoiJT7ZvMepi+MJWXXIS4e1o0ZkwbQqaUayRJYFAoS8PYeKuTRJYl8sC6dsHbNeOuWkZzVr6OvyxLxCYWCBCznHP/5PoPZHyWQk1/M/57Th9+fG06TYDWSJXApFCQgJWcdZMbCWL5N2YunR1sevXQI/Tq39HVZIj6nUJCAkl9UwkurNvPyqs00CW7AY5cO4UpPdzWSRcopFCRgrE7ezfSFcWzZfYhLhndj+sSBdGzZ2NdlifgVhYLUe3sOFjB7SSLzv8+gR/tmvHPrSM4IVyNZpDIKBam3nHP8OyadR5cmcqigmN+f25f/PaevGskix6BQkHopOSuHqAVxfLdlLyN7tmP2lMGEq5EsclwKBalX8otKeGllMnM+30yzRg154rKhXD4iVI1kES8pFKTe+GrTbmYsjCV1Ty6XnhJC1MQBdGihRrLIiWjgzSAzG29mSWaWbGb3VbLczOz58uXrzSzyiOVBZvaDmUVXV+Ei/7X7YAF3z/uB615bA8C7t43imSuHKxBETsJxjxTMLAh4ETgPSAfWmtli51xChWEXAuHlt1HAnPI//+suIBHQZSal2pSWOt6PSeOxpRvILSzmD2PD+d3ZfdRIFqkCb94+GgkkO+dSAMxsHjAZqBgKk4G3nXMO+NbM2phZV+dcppmFAhOB2cA91Vu+BKqNO3OYviCWtan7GNmrHY9OGULfTi18XZZInedNKIQAaRXup/PLo4CjjQkBMoFngb8Axzz1w8ymAlMBwsLCvChLAlF+UQkvfLaJVz5PoUWThjx5eVkj2UyNZJHq4E0oVPbb5rwZY2aTgCzn3DozO/tYD+KcmwvMBfB4PEduX4QvNu5ixsI4tu3N5bLIUKImRNBefQORauVNKKQD3SvcDwW2eznmcuBiM5sANAFamdn/OeeuO/mSJdBk5eQzKzqRxT9tp3eH5rx3+yhO69PB12WJ1EvehMJaINzMegEZwFXANUeMWQzcWd5vGAVkO+cygb+W3yg/UviTAkG8VVrqmLc2jceXJpJfVMrd48L5n7P70LihGskiNeW4oeCcKzazO4FlQBDwunMu3symlS9/GVgCTACSgVzg5porWQJB0o4cohbEsm7rPsb0bs+sKYPp01GNZJGaZmUnDPkXj8fjYmJifF2G+EBeYQnPf7aJf36RQssmDZkxcSCXRoaokSxyHGa2zjnnqep29Ilm8RurkrK4f1EcaXvzuGJEKH+dMIB2zRv5uiyRgKJQEJ/LOpDPzOgEotdn0qdjc+ZNHc3o3u19XZZIQFIoiM+Uljre+24bf/t4AwXFpdxzXj/uOKu3GskiPqRQEJ9IzDxA1IJYfti2n9P7tmfWJUPo1aG5r8sSCXgKBalVuYXFPLdiE69+uYXWTYP5+5XDuGS4Gski/kKhILVm5YayRnL6vjyuOrU7910YQZtmaiSL+BOFgtS4nQfymflhAh/FZtK3Uwvev2MMI3u183VZIlIJhYLUmJJSx7trtvLkx0kUlJTyp/P7MfXMPjRq6NXXeIiIDygUpEbEb88makEcP6Xt54zwDjwyeTA91UgW8XsKBalWuYXFPPvpJl77agttmwXz3FXDuXhYNzWSReoIhYJUmxWJO3lgUTwZ+/O4emQY942PoHWzYF+XJSInQKEgVbYjO5+HP4xnadwO+nVuwQfTxuDpqUaySF2kUJCTVlLqeOebVJ5avpGiklL+fEF/bj+jtxrJInWYQkFOSlxGNlELYlmfns2Z/Toya/Jgwto383VZIlJFCgU5IYcKinnmk4288fUW2jVvzPNXn8JFQ7uqkSxSTygUxGufJOzkwUVxbM/O59pRYfxlfAStm6qRLFKfKBTkuDKz83hocTzL4ncS0aUlL1wTyYgebX1dlojUAIWCHFVJqeOt1ak8vTyJEue478IIbv1NL4KD1EgWqa8UClKp2PSyRnJsRjZn9evIrEsG072dGski9Z1CQX7hYEExTy9P4q3VqbRv0Zh/XHMKE4eokSwSKBQKctiy+B08tDieHQfyuW5UD/48vj+tmqiRLBJIFApCxv48HlwUz6eJZY3kl66N5JQwNZJFApFCIYAVl5Ty5upUnvlkI85B1IQIbj5djWSRQKZQCFA/pe0nakEs8dsPcG5EJ2ZOHkRoWzWSRQKdQiHA5OQX8fTyjbz1TSodWzRmzrWRjB/cRY1kEQEUCgHDOcey+B08uDierJwCbhjdg3svUCNZRH5JoRAA0vfl8uCieFZsyGJg11a8cr2H4d3b+LosEfFDCoV6rLiklDe+LmskA8yYOICbTutJQzWSReQoFAr11A/b9hG1II7EzAOMG9CJhy5WI1lEjk+hUM8cyC/iqWVJvPPtVjq3bMLL143ggkGd1UgWEa8oFOoJ5xxLYnfw8Ifx7D5YwE2n9eTe8/vTorH+iUXEe3rFqAfS9ubywKI4VibtYnBIK1690cPQ0Da+LktE6iCFQh1WVFLK619t4e+fbqSBGfdPGsiNY3qokSwiJ02hUEet27qP6Qti2bAjh/MHduahiwfRrU1TX5clInWcV/+lNLPxZpZkZslmdl8ly83Mni9fvt7MIst/3t3MVppZopnFm9ld1b0DgSY7r4gZC2O5/OXVZOcV8cr1I5h7g0eBICLV4rhHCmYWBLwInAekA2vNbLFzLqHCsAuB8PLbKGBO+Z/FwL3Oue/NrCWwzsw+OWJd8YJzjuj1mcyMTmDPwQJuPq0X95zfT41kEalW3ryijASSnXMpAGY2D5gMVHxhnwy87ZxzwLdm1sbMujrnMoFMAOdcjpklAiFHrCvHkbY3lxkL4/h84y6GhLTmjZtOZXBIa1+XJSL1kDehEAKkVbifTtlRwPHGhFAeCABm1hM4BVhT2YOY2VRgKkBYWJgXZdV/RSWl/PPLFJ5fsYkgMx66aCDXj+lJUAN95kBEaoY3oVDZK5A7kTFm1gL4D3C3c+5AZQ/inJsLzAXweDxHbj/grNu6l6j5cSTtzGH8oC48ePFAurZW30BEapY3oZAOdK9wPxTY7u0YMwumLBDedc7NP/lSA0N2bhF/W7aB99ZsI6RNU169wcO4gZ19XZaIBAhvQmEtEG5mvYAM4CrgmiPGLAbuLO83jAKynXOZVnZthdeAROfcM9VYd73jnGPxT9t5JDqBfblF3H5GL+4e14/maiSLSC067iuOc67YzO4ElgFBwOvOuXgzm1a+/GVgCTABSAZygZvLVz8duB6INbMfy38W5ZxbUq17Ucdt3XOIGQvj+HLTboaFtubNm0eqkSwiPmFlJwz5F4/H42JiYnxdRo0rLP65kRwc1IA/X9Cf60b3UCNZRE6Yma1zznmquh29N+Eja1P3EjU/lk1ZB5kwpAsPTBpEl9ZNfF2WiAQ4hUIt259byONLNzBvbRohbZry+k0ezo1QI1lE/INCoZY451j0Y1kjeX9eEXec2Zu7xoXTrJH+CUTEf+gVqRak7i5rJH+VvJvh3dvwzpQhDOzWytdliYj8ikKhBhUUlzD38xReWJlM46AGPHLJYK4ZGaZGsoj4LYVCDVmTsofpC+NIzjrIxKFdeXDSQDq1UiNZRPybQqGa7TtUyGNLE3k/Jp3Qtk154+ZTOad/J1+XJSLiFYVCNXHOMf/7DGYvSeRAXhHTzurDXWPDadooyNeliYh4TaFQDVJ2HWTGwjhWb95DZFgbHr10CBFd1EgWkbpHoVAFBcUlvLwqhRdXJtM4uAGzpwzm6lPDaKBGsojUUQqFk/Rtyh6iFsSSsusQFw3rxv2TBtCppRrJIlK3KRRO0N5DhTy6JJEP1qXTvV1T3rplJGf16+jrskREqoVCwUvOOf7zfQazP0ogJ7+Y353dh9+fq0ayiNQvCgUvbN51kOkLYvk2ZS8jerTl0SlD6N+lpa/LEhGpdgqFY8gvKmHOqs3MWbWZJsENeOzSIVzp6a5GsojUWwqFo1idvJvpC+PYsvsQlwzvxvSJA+nYsrGvyxIRqVEKhSPsOVjA7CWJzP8+gx7tm/HOrSM5I1yNZBEJDAqFcs45/h2TzqNLEzlUUMyd5/TlznP70iRYjWQRCRwKBSA5K4eoBXF8t2Uvp/YsaySHd1YjWUQCT0CHQn5RCS+tTGbO55tp1qghf7tsCFeMUCNZRAJXwIbCV5t2M2NhLKl7crn0lBCiJg6gQws1kkUksAVcKOw+WMDsjxJZ8EMGPds3493bRnF63w6+LktExC8ETCiUljrej0njsaUbyC0s5g9jw/nd2X3USBYRqSAgQmHTzhyiFsSyNnUfI3u149Epg+nbSY1kEZEj1etQyC8q4YXPNjH3ixSaN27IE5cP5YoRoZipkSwiUpl6GwpfbNzFjIVxbNuby2WRoURNiKC9GskiIsdU70JhV04Bsz5KYNGP2+ndoTnv3T6K0/qokSwi4o16EwqlpY55a9N4fGki+UWl3D0unGlnqZEsInIi6kUoJO0oaySv27qP0b3bMXvKEPp0bOHrskRE6pw6HQp5hSU8/9km/vlFCi2bNOTpK4ZxaWSIGskiIiepzobCqqQs7l8UR9rePK4YEcpfJwygXfNGvi5LRKROq3OhkHUgn5nRCUSvz6R3x+b86/bRjOnT3tdliYjUC3UmFEpLHe99t42/fbyBguJS7jmvH3ec1ZvGDdVIFhGpLnUiFDbsOMBf58fyw7b9nNanPbMuGUxvNZJFRKqdX4dCbmExz63YxKtfbqF102Ce+e0wppyiRrKISE1p4M0gMxtvZklmlmxm91Wy3Mzs+fLl680s0tt1K7X9R/KeGMATTz7CK5+ncHlkKCvuOYtLI3WJChGRmnTcIwUzCwJeBM4D0oG1ZrbYOZdQYdiFQHj5bRQwBxjl5bqVcDTN3c59zOG683rQd+zEE98zERE5Yd4cKYwEkp1zKc65QmAeMPmIMZOBt12Zb4E2ZtbVy3WPqgkF9F3/jLfDRUSkirzpKYQAaRXup1N2NHC8MSFerguAmU0FpgK0bwqeuQfLlySy7h5b50Wd9VUHYLevi/ADmoefaS5+prn4Wf/q2Ig3oVDZm/jOyzHerFv2Q+fmAnMBzCxmd26Jx4va6j0zi3HOBfxcaB5+prn4mebiZ2YWUx3b8SYU0oHuFe6HAtu9HNPIi3VFRMRPeNNTWAuEm1kvM2sEXAUsPmLMYuCG8rOQRgPZzrlML9cVERE/cdwjBedcsZndCSwDgoDXnXPxZjatfPnLwBJgApAM5AI3H2tdL+qaezI7U09pLspoHn6mufiZ5uJn1TIX5lylb/GLiEgA8urDayIiEhgUCiIiclithkKtXy7Dj1VxLl43sywzi6vdqmvGyc6FmXU3s5Vmlmhm8WZ2V+1XX72qMBdNzOw7M/upfC4erv3qq1dVfkfKlweZ2Q9mFl17VdeMKr5epJpZrJn96NVpq865WrlR1mjeDPSm7FTVn4CBR4yZACyl7PMNo4E13q5bl25VmYvyZWcCkUCcr/fFx8+LrkBk+d9bAhsD9XlRfr9F+d+DgTXAaF/vky/mosLye4D3gGhf748v5wJIBTp4+3i1eaTgs8tl+KGqzAXOuS+AvbVacc056blwzmU6574HcM7lAImUfYq+rqrKXDjn3H8vAxBcfqvLZ5FU6XfEzEKBicCrtVl0DanSXJyo2gyFo10Kw5sx3qxbl1RlLuqbapkLM+sJnELZ/5DrqirNRfnbJT8CWcAnzrmAnQvgWeAvQGkN1VebqjoXDlhuZuus7HJCx1SboVArl8uoI6oyF/VNlefCzFoA/wHuds4dqMbaaluV5sI5V+KcG07ZlQNGmtng6i2vVp30XJjZJCDLOVdfrplW1d+R051zkZRdzfp/zezMYz1YbYZCVS6X4c26dUlV5qK+qdJcmFkwZYHwrnNufg3WWRuq5XnhnNsPrALGV3uFtacqc3E6cLGZpVL2Vsu5ZvZ/NVdqjavS88I5998/s4AFlL0ddXS12CxpCKQAvfi5WTLoiDET+WWz5Dtv161Lt6rMRYXlPakfjeaqPC8MeBt41tf74Qdz0RFoU/73psCXwCRf75Mv5uKIMWdT9xvNVXleNAdaVvj7amD8MR+vlnduAmVniGwGppf/bBowrfzvRtmX8mwGYgHPsdaty7cqzsW/gEygiLL/Idzq6/3xxVwAv6HsEHk98GP5bYKv98dHczEU+KF8LuKAB3y9L76aiyO2UedDoYrPi96UhchPQLw3r526zIWIiBymTzSLiMhhCgURETlMoSAiIocpFERE5DCFgoiIHKZQEBGRwxQKIiJy2P8H1TACwvonUY0AAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot(R,ur, label='numerical')\n", "plot(R, R*exp(-R)*2, '.', label='exact') # with proper normalization, exact solution is 2*r*exp(-r)\n", "legend(loc='best')\n", "show()\n", "\n", "plot(R,ur, '-')\n", "plot(R, R*exp(-R)*2, 'o')\n", "xlim(0,0.05)\n", "ylim(0,0.10)\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly the integration from infinity is stable, and we will use it here.\n", "\n", "Logarithmic mesh is better suited for higher excited states, as they extend far away.\n", "\n", "Lets create a subroutine of what we learned up to now:" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [], "source": [ "def SolveSchroedinger(En,l,R):\n", " ur = integrate.odeint(Schroed_deriv, [0.0,-1e-7], R[::-1], args=(l,En))[:,0][::-1]\n", " ur *= 1./sqrt(integrate.simps(ur**2,x=R))\n", " return ur" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "l=1\n", "n=3\n", "En=-1./(n**2) # 3p orbital\n", "\n", "\n", "#Ri = linspace(1e-6,20,500) # linear mesh already fails for this case\n", "Ri = linspace(1e-6,100,1000)\n", "ui = SolveSchroedinger(En,l,Ri)\n", "plot(Ri,ui,'o-', label='linear');" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "l=1\n", "n=3\n", "En=-1./(n**2) # 3p orbital\n", "\n", "\n", "#Ri = linspace(1e-6,20,500) # linear mesh already fails for this case\n", "Ri = linspace(1e-6,100,1000)\n", "ui = SolveSchroedinger(En,l,Ri)\n", "\n", "\n", "R = logspace(-6,2.,100)\n", "ur = SolveSchroedinger(En,l,R)\n", "\n", "\n", "#ylim([0,0.5])\n", "plot(Ri,ui/Ri,'s-', label='u(r)/r linear')\n", "plot(R,ur/R,'o-', label='u(r)/r logarithmic')\n", "xlim([0,2])\n", "ylim([-0.1,0.4])\n", "legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Shooting algorithm:**\n", "\n", "The boundary condistions are given at two points $a$ and $b$, i.e., $u(a)=u(b)=0$. \n", "\n", "* **Choose $u(a)=0$ and $u'(a)=c$, with $c$ some constant.**\n", "* **Solve for $u(x)$ to the other end, and evaluate $u(b)$.**\n", "\n", "* Using root finding routine find energy $\\varepsilon$ for which u(b)=0. This is the bound state.\n", "* Continue with increasing energy $\\varepsilon$ until sufficient number of bound states is found" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [], "source": [ "def Shoot(En,R,l):\n", " ur = integrate.odeint(Schroed_deriv, [0.0,-1e-7], R[::-1], args=(l,En))[:,0][::-1]\n", " norm=integrate.simps(ur**2,x=R)# normalization is not essential here\n", " ur *= 1./sqrt(norm) # once we normalize, the functions are all of the order of unity\n", " # we know that u(r)~ A r^(l+1), hence, u(r)/r^l ~ A r\n", " ur = ur/R**l\n", " # extrapolate to r=0\n", " f0 = ur[0]\n", " f1 = ur[1]\n", " f_at_0 = f0 + (f1-f0)*(0.0-R[0])/(R[1]-R[0])\n", " return f_at_0" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-9.51622801467704e-09, 4077.4668824451173)" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R = logspace(-6,2.2,500)\n", "\n", "Shoot(-1.,R,0), Shoot(-1/3**2, R, l=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Shooting algorithm:**\n", "\n", "The boundary condistions are given at two points $a$ and $b$, i.e., $u(a)=u(b)=0$. \n", "\n", "* Choose $u(a)=0$ and $u'(a)=c$, with $c$ some constant.\n", "* Solve for $u(x)$ to the other end, and evaluate $u(b)$.\n", "\n", "* **Using root finding routine find energy $\\varepsilon$ for which u(b)=0. This is the bound state.**\n", "* **Continue with increasing energy $\\varepsilon$ until sufficient number of bound states is found**" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [], "source": [ "def FindBoundStates(R,l,nmax,Esearch):\n", " \"\"\" R -- real space mesh\n", " l -- orbital quantum number\n", " nmax -- maximum number of bounds states we require\n", " Esearch -- energy mesh, which brackets all bound-states, i.e., every sign change of the wave function at u(0).\n", " \"\"\"\n", " n=0\n", " Ebnd=[] # save all bound states\n", " u0 = Shoot(Esearch[0],R,l) # u(r=0) for the first energy Esearch[0]\n", " for i in range(1,len(Esearch)):\n", " u1 = Shoot(Esearch[i],R,l) # evaluate u(r=0) and all Esearch points\n", " if u0*u1<0:\n", " Ebound = optimize.brentq(Shoot,Esearch[i-1],Esearch[i],xtol=1e-16,args=(R,l)) # root finding routine\n", " Ebnd.append((l,Ebound))\n", " if len(Ebnd)>nmax: break\n", " n+=1\n", " print('Found bound state at E=%14.9f E_exact=%14.9f l=%d' % (Ebound, -1.0/(n+l)**2,l))\n", " u0=u1\n", " \n", " return Ebnd" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-1.2 , -0.83333333, -0.6122449 , -0.46875 , -0.37037037,\n", " -0.3 , -0.24793388, -0.20833333, -0.17751479, -0.15306122,\n", " -0.13333333, -0.1171875 , -0.10380623, -0.09259259, -0.08310249,\n", " -0.075 , -0.06802721, -0.06198347, -0.05671078, -0.05208333,\n", " -0.048 , -0.0443787 , -0.04115226, -0.03826531, -0.03567182,\n", " -0.03333333, -0.03121748, -0.02929688, -0.02754821, -0.02595156,\n", " -0.0244898 , -0.02314815, -0.02191381, -0.02077562, -0.01972387,\n", " -0.01875 , -0.01784652, -0.0170068 , -0.01622499, -0.01549587,\n", " -0.01481481, -0.01417769, -0.01358081, -0.01302083, -0.01249479,\n", " -0.012 , -0.01153403, -0.01109467, -0.01067996, -0.01028807,\n", " -0.00991736, -0.00956633, -0.00923361, -0.00891795, -0.00861821,\n", " -0.00833333, -0.00806235, -0.00780437, -0.00755858, -0.00732422,\n", " -0.00710059, -0.00688705, -0.006683 , -0.00648789, -0.0063012 ,\n", " -0.00612245, -0.0059512 , -0.00578704, -0.00562957, -0.00547845,\n", " -0.00533333, -0.00519391, -0.00505988, -0.00493097, -0.00480692,\n", " -0.0046875 , -0.00457247, -0.00446163, -0.00435477, -0.0042517 ,\n", " -0.00415225, -0.00405625, -0.00396354, -0.00387397, -0.0037874 ,\n", " -0.0037037 , -0.00362275, -0.00354442, -0.00346861, -0.0033952 ,\n", " -0.0033241 , -0.00325521, -0.00318844, -0.0031237 , -0.00306091])" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Esearch = -1.2/arange(1,20,0.2)**2\n", "Esearch" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Found bound state at E= -1.000000018 E_exact= -1.000000000 l=0\n", "Found bound state at E= -0.249999997 E_exact= -0.250000000 l=0\n", "Found bound state at E= -0.111111111 E_exact= -0.111111111 l=0\n", "Found bound state at E= -0.062500000 E_exact= -0.062500000 l=0\n", "Found bound state at E= -0.040000002 E_exact= -0.040000000 l=0\n", "Found bound state at E= -0.027777593 E_exact= -0.027777778 l=0\n", "Found bound state at E= -0.020376800 E_exact= -0.020408163 l=0\n", "Found bound state at E= -0.249999997 E_exact= -0.250000000 l=1\n", "Found bound state at E= -0.111111112 E_exact= -0.111111111 l=1\n", "Found bound state at E= -0.062500001 E_exact= -0.062500000 l=1\n", "Found bound state at E= -0.040000003 E_exact= -0.040000000 l=1\n", "Found bound state at E= -0.027777889 E_exact= -0.027777778 l=1\n", "Found bound state at E= -0.020421586 E_exact= -0.020408163 l=1\n", "Found bound state at E= -0.111111111 E_exact= -0.111111111 l=2\n", "Found bound state at E= -0.062500001 E_exact= -0.062500000 l=2\n", "Found bound state at E= -0.040000004 E_exact= -0.040000000 l=2\n", "Found bound state at E= -0.027778516 E_exact= -0.027777778 l=2\n", "Found bound state at E= -0.020414271 E_exact= -0.020408163 l=2\n", "Found bound state at E= -0.062500000 E_exact= -0.062500000 l=3\n", "Found bound state at E= -0.040000001 E_exact= -0.040000000 l=3\n", "Found bound state at E= -0.027778126 E_exact= -0.027777778 l=3\n", "Found bound state at E= -0.020405512 E_exact= -0.020408163 l=3\n", "Found bound state at E= -0.040000000 E_exact= -0.040000000 l=4\n", "Found bound state at E= -0.027777799 E_exact= -0.027777778 l=4\n", "Found bound state at E= -0.020410583 E_exact= -0.020408163 l=4\n", "Found bound state at E= -0.027777787 E_exact= -0.027777778 l=5\n", "Found bound state at E= -0.020406833 E_exact= -0.020408163 l=5\n" ] } ], "source": [ "Esearch = -1.2/arange(1,20,0.2)**2\n", "R = logspace(-6,2.2,500)\n", "nmax=7\n", "\n", "Bnd=[]\n", "for l in range(nmax-1):\n", " Bnd += FindBoundStates(R,l,nmax-l,Esearch)" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(0, -1.0000000175237596),\n", " (0, -0.24999999672098724),\n", " (0, -0.111111111078589),\n", " (0, -0.06250000038883327),\n", " (0, -0.04000000224162835),\n", " (0, -0.027777592625265607),\n", " (0, -0.02037679979082838),\n", " (0, -0.015338082264993079),\n", " (1, -0.24999999669248538),\n", " (1, -0.11111111161935987),\n", " (1, -0.06250000145629958),\n", " (1, -0.04000000294999124),\n", " (1, -0.02777788871522449),\n", " (1, -0.020421586294454935),\n", " (1, -0.015413169414010558),\n", " (2, -0.11111111126358454),\n", " (2, -0.06250000053821902),\n", " (2, -0.04000000419609433),\n", " (2, -0.027778515786204303),\n", " (2, -0.020414270711048885),\n", " (2, -0.015484354553810139),\n", " (3, -0.062499999809768725),\n", " (3, -0.04000000123306967),\n", " (3, -0.027778125963890867),\n", " (3, -0.02040551166885938),\n", " (3, -0.015519806412257295),\n", " (4, -0.03999999995489171),\n", " (4, -0.02777779850099041),\n", " (4, -0.020410582926272625),\n", " (4, -0.015576802781241739),\n", " (5, -0.027777787425614712),\n", " (5, -0.020406832575417415),\n", " (5, -0.015601410734192005)]" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Bnd" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(0, -1.0000000175237596),\n", " (0, -0.24999999672098724),\n", " (1, -0.24999999669248538),\n", " (1, -0.11111111161935987),\n", " (2, -0.11111111126358454),\n", " (0, -0.111111111078589),\n", " (1, -0.06250000145629958),\n", " (2, -0.06250000053821902),\n", " (0, -0.06250000038883327),\n", " (3, -0.062499999809768725),\n", " (2, -0.04000000419609433),\n", " (1, -0.04000000294999124),\n", " (0, -0.04000000224162835),\n", " (3, -0.04000000123306967),\n", " (4, -0.03999999995489171),\n", " (2, -0.027778515786204303),\n", " (3, -0.027778125963890867),\n", " (1, -0.02777788871522449),\n", " (4, -0.02777779850099041),\n", " (5, -0.027777787425614712),\n", " (0, -0.027777592625265607),\n", " (1, -0.020421586294454935),\n", " (2, -0.020414270711048885),\n", " (4, -0.020410582926272625),\n", " (5, -0.020406832575417415),\n", " (3, -0.02040551166885938),\n", " (0, -0.02037679979082838),\n", " (5, -0.015601410734192005),\n", " (4, -0.015576802781241739),\n", " (3, -0.015519806412257295),\n", " (2, -0.015484354553810139),\n", " (1, -0.015413169414010558),\n", " (0, -0.015338082264993079)]" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sorted(Bnd, key= lambda x: x[1])" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [], "source": [ "def cmpKey(x):\n", " return x[1] + x[0]/10000. # energy has large wait, but degenerate energy states are sorted by l\n", "\n", "Bnd = sorted(Bnd, key=cmpKey)" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(0, -1.0000000175237596),\n", " (0, -0.24999999672098724),\n", " (1, -0.24999999669248538),\n", " (0, -0.111111111078589),\n", " (1, -0.11111111161935987),\n", " (2, -0.11111111126358454),\n", " (0, -0.06250000038883327),\n", " (1, -0.06250000145629958),\n", " (2, -0.06250000053821902),\n", " (3, -0.062499999809768725),\n", " (0, -0.04000000224162835),\n", " (1, -0.04000000294999124),\n", " (2, -0.04000000419609433),\n", " (3, -0.04000000123306967),\n", " (4, -0.03999999995489171),\n", " (0, -0.027777592625265607),\n", " (1, -0.02777788871522449),\n", " (2, -0.027778515786204303),\n", " (3, -0.027778125963890867),\n", " (4, -0.02777779850099041),\n", " (5, -0.027777787425614712),\n", " (0, -0.02037679979082838),\n", " (1, -0.020421586294454935),\n", " (2, -0.020414270711048885),\n", " (3, -0.02040551166885938),\n", " (4, -0.020410582926272625),\n", " (5, -0.020406832575417415),\n", " (0, -0.015338082264993079),\n", " (1, -0.015413169414010558),\n", " (2, -0.015484354553810139),\n", " (3, -0.015519806412257295),\n", " (4, -0.015576802781241739),\n", " (5, -0.015601410734192005)]" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Bnd" ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "adding state ( 0, -1.000000018) with fermi=1.00 and current N= 2.0\n", "adding state ( 0, -0.249999997) with fermi=1.00 and current N= 4.0\n", "adding state ( 1, -0.249999997) with fermi=1.00 and current N= 10.0\n", "adding state ( 0, -0.111111111) with fermi=1.00 and current N= 12.0\n", "adding state ( 1, -0.111111112) with fermi=1.00 and current N= 18.0\n", "adding state ( 2, -0.111111111) with fermi=1.00 and current N= 28.0\n", "adding state ( 0, -0.062500000) with fermi=1.00 and current N= 30.0\n", "adding state ( 1, -0.062500001) with fermi=1.00 and current N= 36.0\n", "adding state ( 2, -0.062500001) with fermi=1.00 and current N= 46.0\n" ] } ], "source": [ "Z=46 # like Ni\n", "N=0\n", "rho=zeros(len(R))\n", "for (l,En) in Bnd:\n", " ur = SolveSchroedinger(En,l,R)\n", " dN = 2*(2*l+1) # each radial function can store these many electrons\n", " if N+dN<=Z:\n", " ferm = 1. # no fractional occupancy needed\n", " else:\n", " ferm = (Z-N)/float(dN) # fractional occupancy, because the orbital is not fully filled\n", " drho = ur**2 * ferm * dN/(4*pi*R**2) # charge density per solid angle per radius: drho/(dOmega*dr)\n", " rho += drho\n", " N += dN\n", " print('adding state (%2d,%14.9f) with fermi=%4.2f and current N=%5.1f' % (l,En,ferm,N))\n", " if N>=Z: break" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Resulting charge density for a Ni-like Hydrogen atom" ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from pylab import *\n", "%matplotlib inline\n", "\n", "plot(R,rho*4*pi*R**2,label='charge density')\n", "xlim([0,60])\n", "show()" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "45.99999999999999" ] }, "execution_count": 99, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integrate.simpson(rho*R**2 * 4*pi,x=R) # total density" ] }, { "cell_type": "code", "execution_count": 114, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "l,En=3,-1/4**2\n", "#l,En = Bnd[9]\n", "#R = logspace(-6,2,1000)\n", "R = logspace(-2,2.5,1000)\n", "ur = SolveSchroedinger(En,l,R)\n", "\n", "plot(R,ur,'-');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It seems that error accumulation still prevents one to calculate f-states near the nucleous. Only if we start sufficiently away from nucleout (0.1$R_b$) numerics works.\n", "\n", "Can we do better?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerov algorithm\n", "\n", "The general purpose integration routine is not the best method for solving the Schroedinger equation, which does not have first derivative terms. \n", "\n", "Numerov algorithm is better fit for such equations, and its algorithm is summarized below. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The second order linear differential equation (DE) of the form\n", "\n", "\\begin{eqnarray}\n", " x''(t) = f(t) x(t) + u(t)\n", "\\end{eqnarray}\n", "\n", "is a target of Numerov algorithm.\n", "\n", "Due to a special structure of the DE, the fourth order error cancels\n", "and leads to sixth order algorithm using second order integration\n", "scheme.\n", "\n", "\n", "If we expand x(t) to some higher power and take into account the time\n", "reversal symmetry of the equation, all odd term cancel\n", "\n", "\\begin{eqnarray}\n", " x(h) = x(0)+h x'(0)+\\frac{1}{2}h^2 x''(0)+\\frac{1}{3!}h^3\n", " x^{(3)}(0)+\\frac{1}{4!}h^4 x^{(4)}(0)+\\frac{1}{5!}h^5 x^{(5)}(0)+...\\\\\n", " x(-h) = x(0)-h x'(0)+\\frac{1}{2}h^2 x''(0)-\\frac{1}{3!}h^3\n", " x^{(3)}(0)+\\frac{1}{4!}h^4 x^{(4)}(0)-\\frac{1}{5!}h^5\n", " x^{(5)}(0)+...\n", "\\end{eqnarray}\n", "\n", "hence \n", "\n", "\\begin{eqnarray}\n", " x(h)+x(-h) = 2x(0)+h^2 (f(0)x(0)+u(0))+\\frac{2}{4!}h^4 x^{(4)}(0)+O(h^6)\n", "\\end{eqnarray}\n", "\n", "\n", "If we are happy with $O(h^4)$ algorithm, we can neglect $x^{(4)}$ term and\n", "get the following recursion relation\n", "\n", "\\begin{equation}\n", " x_{i+1} = 2 x_i - x_{i-1} + h^2 (f_i x_i+u_i) +O(h^4).\n", "\\end{equation}\n", "where we renaimed\n", "\\begin{eqnarray}\n", "&x_{i-1}&= x(-h)\\\\\n", "&x_i &= x(0)\\\\\n", "&x_{i+1} &= x(h)\n", "\\end{eqnarray}\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But we know from the differential equation that\n", "\n", "\\begin{equation}\n", " x^{(4)} = \\frac{d^2 x''(t)}{dt^2} = \\frac{d^2}{dt^2}(f(t) x(t)+u(t))\n", "\\end{equation}\n", "and we will use the well known descrete expression for the second order derivative\n", "\\begin{eqnarray}\n", "g''(t) = \\frac{g(t+h) - 2 g(t) + g(t-h)}{h^2} + O(h^2)\n", "\\end{eqnarray}\n", "which can be approximated by\n", "\n", "\\begin{equation}\n", " x^{(4)}= \\frac{f_{i+1}x_{i+1}+u_{i+1}-2 f_i x_i -2 u_i+ f_{i-1}x_{i-1}+u_{i-1}}{h^2} + O(h^2)\n", "\\end{equation}\n", "\n", "Inserting the fourth order derivative into the above recursive equation (forth equation in his chapter), we\n", "get\n", "\n", "\\begin{equation}\n", " x_{i+1}-2 x_i+x_{i-1}=h^2(f_i x_i+u_i)+\\frac{h^2}{12}(f_{i+1}x_{i+1}+u_{i+1}-2 f_i x_i -2 u_i+ f_{i-1}x_{i-1}+u_{i-1}) + O(h^6)\n", "\\end{equation}\n", "\n", "If we switch to a new variable $w_i=x_i(1-\\frac{h^2}{12} f_i)-\\frac{h^2}{12}u_i$\n", "we are left with the following\n", "equation\n", "\n", "\\begin{equation}\n", " w_{i+1} = 2 w_i - w_{i-1} + h^2 (f_i x_i + u_i)+O(h^6)\n", "\\end{equation}\n", "\n", "The variable $x$ needs to be recomputed at each step with\n", "\\begin{equation}\n", "x_i=\\frac{w_i+\\frac{h^2}{12}u_i}{1-\\frac{h^2}{12}f_i}.\n", "\\end{equation}\n", "\n" ] }, { "cell_type": "code", "execution_count": 115, "metadata": {}, "outputs": [], "source": [ "@jit(nopython=True)\n", "def Numerovc(f, x0, dx, dh):\n", " \"\"\"Given precomputed function f(x), solves for x(t), which satisfies:\n", " x''(t) = f(t) x(t)\n", " dx = (dx(t)/dt)_{t=0}\n", " x0 = x(t=0)\n", " \"\"\"\n", " x = zeros(len(f))\n", " x[0] = x0\n", " x[1] = x0+dh*dx\n", " h2 = dh**2\n", " h12 = h2/12.\n", " w0=x0*(1-h12*f[0])\n", " w1=x[1]*(1-h12*f[1])\n", " xi = x[1]\n", " fi = f[1]\n", " for i in range(2,f.size):\n", " w2 = 2*w1-w0+h2*fi*xi # here fi,xi=f1,x1 at the first step\n", " fi = f[i] # at this point fi=f2 in the first step\n", " xi = w2/(1-h12*fi) # xi is not x2 in the first step\n", " x[i]=xi # save x2 into x[2]\n", " w0,w1 = w1,w2\n", " return x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For Numerov algorithm we can evaluate derivative part $f(r)$ for all points at once:\n", "\n", "Because Schroedinger Eq is:\n", "\\begin{eqnarray}\n", "u''(r)=\n", "\\left(\\frac{l(l+1)}{r^2}-\\frac{2Z}{r}-\\varepsilon\\right)u(r)\n", "\\end{eqnarray}\n", "the $f$ function is\n", "\\begin{eqnarray}\n", "f(r)=\n", "\\left(\\frac{l(l+1)}{r^2}-\\frac{2Z}{r}-\\varepsilon\\right)\n", "\\end{eqnarray}\n" ] }, { "cell_type": "code", "execution_count": 116, "metadata": {}, "outputs": [], "source": [ "def fSchrod(En, l, R):\n", " return l*(l+1.)/R**2-2./R-En" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Numerov algorithm is much faster, but the price we pay is the mesh has to be linear. We can not use logarithmic mesh in combination with Numerov algorithm." ] }, { "cell_type": "code", "execution_count": 117, "metadata": {}, "outputs": [], "source": [ "Rl = linspace(1e-6,100,1000)\n", "l,En=0,-1\n", "f = fSchrod(En,l,Rl[::-1]) # here we turn mesh R around, so that f is given from large r down to r=0.\n", "ur = Numerovc(f,0.0,1e-7,Rl[1]-Rl[0])[::-1] # turn around the solution, so that it starts with r=0\n", "norm = integrate.simps(ur**2,x=Rl)\n", "ur *= 1/sqrt(abs(norm))" ] }, { "cell_type": "code", "execution_count": 120, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 10.0)" ] }, "execution_count": 120, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from pylab import *\n", "%matplotlib inline\n", "\n", "plot(Rl,ur)\n", "plot(Rl,exp(-Rl)*Rl*2.);\n", "xlim(0,10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Numerov seems much more precise than odeint, and avoids numerical problems we had before" ] }, { "cell_type": "code", "execution_count": 125, "metadata": {}, "outputs": [ { "data": { "image/png": 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0278rLZrV0gt4XXsBSnWZBoCb7Tp5gaZmowHgYpPT4pmSFs8L2gtQqss0ANxsW8F5bAHChIG9rC7F5zw1K117AUp1gwaAm211jP9HhARaXYrP0V6AUt2jAeBGlxqa2Fek4//udLkX8NrWk1aXopTX0QBwo90nK2i06/i/O33WCyigtkF7AUp1hgaAG20tKNfx/x6waFY6ZdX1vL5NewFKdYYGgBvp+H/PmJQWz9TB2gtQqrM0ANzk8vj/pEE6/NMTnrpRewFKdZYGgJt8Nv4fZ3UpfuGzXsAx7QUo5SSnAkBE5ohIrojki8jidp4fJiJbRKReRL7e5rkTInJARPaKyE5XFe7pPh3/T9UA6CmLZg2lrLpBewFKOanDABARG7AEmAtkAveISGab1c4DTwLPfc7LzDTGjDHGTOhOsd5ka0E51yTHEKnj/z1m4qA4pg3RXoBSznKmBzARyDfGFBhjGoDlwLzWKxhjSo0xO4BGN9TodfT4f+s8dWNLL0DPC1CqY84EQDJQ2OpxkWOZswywVkR2iciCzhTnrXT83zqXewEvfnyMSw1NVpejlEdzZnxC2llmOvEe04wxxSKSCKwTkSPGmI+veJOWcFgAkJCQQHZ2difewrO8m9dAgEBtYQ7ZZw7903PV1dVe3baOeEL7ZsTb2ZzfwPdf38DcQa6dgtsT2udO2j7/4kwAFAH9Wz1OAYqdfQNjTLHjtlRE3qdlSOmKADDGLAWWAmRkZJisrCxn38LjLDnyCaNSDHNnTbviuezsbLy5bR3xhPZlARvPb2NtYSXP3DPNpddh8IT2uZO2z784MwS0A0gXkUEiEgzcDaxw5sVFJEJEoi7fB24GDna1WG9Q22Bnr87/b7mv35zBhUuNLNt43OpSlPJYHQaAMaYJeAJYAxwG3jLG5IjIQhFZCCAiSSJSBPwH8IyIFIlINNAH2CQi+4DtwEpjzGp3NcYT7D51Qcf/PcDo/rHMHZnEso0FlFfXW12OUh7JqWMUjTGrgFVtlr3Q6n4JLUNDbV0ERnenQG+jx/97jv+8eShrckpYsuEYz97W9shlpZSeCexiWwvKGanH/3uEIYlR3Dk+hde2nuR0Ra3V5SjlcTQAXOiz8X/99u8pnpo1FIBfrjtqcSVKeR4NABf6bPxfdwB7iuTYMOZPGci7u4vIL62yuhylPIoGgAvp/P+e6atZgwkLsvGztdoLUKo1DQAXujz+78rjzlX3xUeG8Oh1afztYAn7CiusLkcpj6EB4CI6/u/ZHr1uEHERwfzfmlyrS1HKY2gAuIiO/3u2qNAgvpo1mE35ZWzMO2d1OUp5BA0AF9mm4/8eb/6UgaT0CuNHq45gb+7MdFZK+SYNABfZWnBex/89XEigjafnDOPwmYu8v+e01eUoZTkNABf4dPx/kI7/e7rbRvVldP9YnluTqxeNUX5PA8AF9py6QIO9Wcf/vYCI8O0vDKfkYh0vbSqwuhylLKUB4AJbC8oJEJiQquP/3mDioDhmj+jD89nHOFelE8Up/6UB4AJbC85zjY7/e5VvzhlGfVMzv/y7nhym/JcGQDfp/P/eKS0hkvsmD2T5jkLyzuoUEco/aQB0k47/e68nb0wnPMjGT/52xOpSlLKEBkA36fi/94qLCObxG4bw0ZFSNueXWV2OUj1OA6CbdPzfuz04NZX+cWF8/8McGu3NVpejVI/SAOgGHf/3fqFBNr5zSyZHz1bz2taTVpejVI/SAOgGHf/3DTdl9uG69N78fN1RvX6w8isaAN2w9fh5Hf/3ASLCd2/LpLbBznNrdbZQ5T80ALpB5//3HUMSo3hwairLdxRyoKjS6nKU6hEaAF1U12hn7ykd//clT85KJz4imO+uOIgxOluo8n0aAF20+9Pxf50AzldEhwbx9Jxh7D5VwQd7dbZQ5fs0ALpoa8Hl8X8NAF9y57gURqfE8ONVR6iub7K6HKXcSgOgiy6P/0fr+L9PCQgQvnf7CM5V1/OLdTpPkPJtGgBdoOP/vm3sgF7cM3EAr2w+zsHTukNY+S4NgC7Q8X/f983Zw4iLCObb7x/Qy0cqn6UB0AU6/u/7YsKD+M6tmewrquT1bXqGsPJNGgBdsLWgnBH9dPzf190+uh/Th/Tm/1bncvZindXlKOVyTgWAiMwRkVwRyReRxe08P0xEtohIvYh8vTPbepvPxv/127+vExF+8MWR1Nub+e+/HrK6HKVcrsMAEBEbsASYC2QC94hIZpvVzgNPAs91YVuvslvn//Erqb0j+PeZQ1i5/wzZuaVWl6OUSznTA5gI5BtjCowxDcByYF7rFYwxpcaYHUBjZ7f1Njr+738WzEhjcEIE337/ILVNukNY+Y5AJ9ZJBgpbPS4CJjn5+k5vKyILgAUACQkJZGdnO/kWPWv17loGRgWwZ9vmLm1fXV3tsW1zBV9t391pdn60rY4/5xjCArOtLsdtfPX3d5mvt6+znAkAaWeZs1+DnN7WGLMUWAqQkZFhsrKynHyLnlPbYOf4ujU8PG0QWVnDu/Qa2dnZeGLbXMVX25cFnAk8xMubj/PVW69hymDfHAL01d/fZb7evs5yZgioCOjf6nEKUOzk63dnW4+z8+R5Gu2GyT76x6+u7huzM0gMF7757n4uNeg0Ecr7ORMAO4B0ERkkIsHA3cAKJ1+/O9t6nC3HyrEFCNfq+L9fCgu28cjIEE6dv8RPV+t1A5T36zAAjDFNwBPAGuAw8JYxJkdEForIQgARSRKRIuA/gGdEpEhEoj9vW3c1xt22FJQzKiWGyBBnRs6UL8qIs/HAlIG8uuUEO06ct7ocpbrFqU8yY8wqYFWbZS+0ul9Cy/COU9t6o+r6JvYXVfLY9WlWl6Is9vScYazPLeXpd/az6snrCAu2WV2SUl2iZwI7aceJ89ibDVMH97a6FGWxiJBA/veOURwvq+HHfztsdTlKdZkGgJO2HisnyCaMH6jX/1UwdUhvHpk+iD9uOcmGI3qCmPJOGgBO2lJQztj+vbS7rz71jdkZDEuK4hvv7KOsut7qcpTqNA0AJ1ysa+Tg6Uo9/FP9k9AgG7+6eywX65r45jv79TrCyutoADhhe8F5mg1M0fl/VBsZSVEsnjOMj46U8vq2U1aXo1SnaAA4YUtBOcGBAYwdEGt1KcoDPTg1levSe/ODlYfIL622uhylnKYB4IQtx8oZP6AXoUE6/q+uFBAg/OxLowkLsvHkG3uoa7RbXZJSTtEA6EDFpQYOl1z02blflGskRofys38dzaEzF/XaAcpraAB0YGvBeYxBA0B16IZhfXhsRhp/3naKv+w9bXU5SnVIA6ADm/LPERFsY0z/WKtLUV7g6zdncG1qL7713gHdH6A8ngZABzbmlTFlcDxBNv2nUh0LsgXwm3vGERpk46uv76K2QfcHKM+ln2pXUXj+EifLLzF9iE7/oJyXFBPKL+8aQ15pNf/1/gE9P0B5LA2Aq9iYVwbA9PQEiytR3ub6oQksunEo7+85zUubjltdjlLt0gC4ik355+gbE8rghAirS1Fe6N9vGMLNmX340arDbHJ8mVDKk2gAfA57s2FzfjnTh/RGpL0rWyp1dQEBws/vGsOQxEieeGM3p8ovWV2SUv9EA+BzHDhdSWVtI9cN1eEf1XWRIYEsnT+B5mbDgj/tpKZeLyWpPIcGwOfYlHcOgGl6/L/qptTeEfzmy+M4eraKRW/uxd6sO4WVZ9AA+Bwb88oY0S+a+MgQq0tRPmDG0AS+c2sm6w6d5Ycr9SIyyjNoALSjpr6J3acuMD1dD/9UrvPQtEE8ODWVlzcf5w+b9cggZT29unk7th8/T6PdcL0e/qlc7Du3ZlJ0oZb//ushknuFc1NmH6tLUn5MewDt+DjvHCGBAXr5R+VytgDh1/eMYWRyDE++sYd9hRVWl6T8mAZAO/6Re47JafE6/bNyi/DgQJY9MIH4yGAefGU7+aVVVpek/JQGQBsnymooKKvhhmGJVpeifFhiVCivPTIJW0AA9y3bTtEFPUdA9TwNgDbWHykF0ABQbpfaO4I/PTKRSw1NzH9pO+eq9MLyqmdpALSxIbeUIYmR9I8Lt7oU5QeG943mlYeupaSyjvtf3k7lpUarS1J+RAOgler6JrYVnNdv/6pHjR8Yx4vzx5NfWsX8l7dpCKgeowHQyqa8MhrszczM0ABQPev6oQm8cN94jpyp4r6XNARUz9AAaGXDkVKiQgOZkKqHf6qed+PwPrwwfxy5JRoCqmc4FQAiMkdEckUkX0QWt/O8iMivHc/vF5FxrZ47ISIHRGSviOx0ZfGuZIxhQ24p16cn6NW/lGVuGNaHF+ePJ7ekintf2sqFmgarS1I+rMNPOhGxAUuAuUAmcI+IZLZZbS6Q7vhZADzf5vmZxpgxxpgJ3S/ZPXKKL1JaVc9MHf9XFps5LJEX54/n6NlqvvTiFs5U1lpdkvJRznzVnQjkG2MKjDENwHJgXpt15gF/NC22ArEi0tfFtbrVR4dLEYGsDJ3+QVlv5rBEXn1oIiWVddz5/BYKzukF5pXrOTMXUDJQ2OpxETDJiXWSgTOAAdaKiAFeNMYsbe9NRGQBLb0HEhISyM7OdqZ+l3lnWy3psQEc3LnFre9TXV3d423rSdo+1/r6uEB+tquWeb/5B/85PpTUGPeena6/P//iTAC0dzmsthOaX22dacaYYhFJBNaJyBFjzMdXrNwSDEsBMjIyTFZWlhOlucbJ8hoKV2fzzC3Dybouza3vlZ2dTU+2radp+1zv+qnVzH9pO8/tbmTJvaOY4caLFOnvz784MwRUBPRv9TgFKHZ2HWPM5dtS4H1ahpQ8ypqcEgBmj0iyuBKlrpSWEMm7X5lK/7hwHv7DDv609aTVJSkf4UwA7ADSRWSQiAQDdwMr2qyzArjfcTTQZKDSGHNGRCJEJApARCKAm4GDLqzfJVYfLGFkcrSe/as8VlJMKO8snELW0AS+88FBvv9hjl5ZTHVbhwFgjGkCngDWAIeBt4wxOSKyUEQWOlZbBRQA+cDvga86lvcBNonIPmA7sNIYs9rFbeiW0ot17D5VwexM/favPFtESCBL75/Aw9MG8crmEyz4404u1um5AqrrnLogjDFmFS0f8q2XvdDqvgEeb2e7AmB0N2t0qzWHzgIwZ6QGgPJ8tgDh2dsySUuI4Hsrcpj32828cN94MpKirC5NeSG/P+Np1f4zpCVEMCQx0upSlHLafZMH8saCyVTXN/HFJZtZsa/tbjmlOubXAVBSWcfW4+XcProfIu0dyKSU57o2NY6V/z6dkcnRPPnGHr7/YQ71TXary1JexK8D4MN9xRgDt4/uZ3UpSnVJYnQof/63yZ/uF7jjd59wTE8aU07y6wD4y77TjEqJIS1Bh3+U9wqyBfDsbZksu38CxRW13PrrTSzffoqWXXNKfT6/DYD80moOnr7IvDHJVpeilEvMyuzD6kXXM35gLxa/d4CvvLZbrzKmrspvA2DF3tMECNw2yqumLFLqqvpEh/LHhyfyX18YxvrcUm76xT94f0+R9gZUu/wyAJqbDR/sLWbq4N4kRodaXY5SLhUQICy4fjCrnryOtN4RfO3NfTzy6k6dVVRdwS8DYGtBOafOX+KOcTr8o3zXkMRI3l44lWdvzWTLsXJu/vnHvLL5OE32ZqtLUx7CLwPgz9tPERMWxBeu0eEf5dtsAcLD0wexZtH1jBkQy/c/PMQtv97ElmPlVpemPIDfBUB5dT1rckq4Y1wyoUHunVpXKU8xID6cPz48kRfuG091fRP3/H4rj/95N8UVOizkz5yaCsKXvLu7iEa74Z6JA6wuRakeJSLMGZlEVkYCL/zjGM9nH+Pvh87y4LRUvjJjMLHhwVaXqHqYXwWAMYY3thcyYWAvhvbRuVOUfwoNsrFo1lD+ZVwKv1h3lKUfF/DGtlMszBrMYLseLeRP/CoANuaVcbyshidmDrG6FKUs1z8unJ/fNYYFM9J4bk0uP12dS2yIUBhcwJcnDSA82K8+HvySX+0D+P3GAhKiQrh1tO78VeqyYUnRLHvgWt5eOIWkCOEHKw8z7Sfr+c1HeVTW6nTTvsxvAuDwmYtszCvjwamphATqzl+l2ro2NY7FE8N49ytTGDugFz9bd5RpP1nPj1cdpvD8JavLU27gN328ZRuPEx5s495JuvNXqasZPzCOlx+MI6e4kuezj7Fs03F+v7GAG4f34cGpqUwdHK+z5/oIvwiAE2U1fLD3NPdPGahHOijlpBH9Yvjtl8dRXFHL69tO8sb2QtYdOkt6YiTzpwzk9tH99O/Jy/nFENCv1+cRZBO+kjXY6lKU8jr9YsP4xuxhfLL4Bp770mhCg2w8+5ccJv7wIx5/fTcbjpTq2cVeyud7APml1Xyw5zSPXpdGYpTO+6NUV4UG2bhzfAp3jk8hp7iSd3YV8Ze9xaw8cIaEqBDmje7HF0b1ZWz/WB0i8hI+HwA/+dsRwoJsPHZ9mtWlKOUzRvSLYUS/GL41dzgbckt5e2cRr245wbJNx+kXE8qckX25ZVQSY/v3IiBAw8BT+XQAZOeW8vfDZ1k8dxjxkSFWl6OUzwkODGD2iCRmj0iisraRjw6fZdWBM7y29SQvbz5OQlQIWUMTmDkskenpvYkODbK6ZNWKzwZAfZOd//7wEGm9I3h42iCry1HK58WEBXHHuBTuGJdCVV0jHx1u+QK2JqeEt3cVYQsQxg/sxcyMRKYNiSezbzSBNr/YDemxfDYAfr7uKAVlNbz68ESCA/U/mVI9KSo0iC+OTeaLY5Npsjezp7CC7NxSNhw5x/+uPtKyTkggE1J7MTktnklp8Yzsp4HQ03wyALYVlLP04wLumTiAGUMTrC5HKb8WaAvg2tQ4rk2N4xuzh1F6sY6tx8+ztaCcbQXlbMg9B0B4sI1rkmMY0z+W0Y6ffjGhukPZjXwuAEqr6vjam3sZGBfOM7cMt7ocpVQbidGh3D66H7eP7ge0/M1uP36enScusLewglc2n6DBcVhpQlQIo1NiGN43moykKIYlRZEaH6E9BRfxqQCobbDzb6/u5MKlRt5eOIWIEJ9qnlI+KTEqlFtH9ePWUS2BUN9k58iZKvYVVbC3sIL9RZVsyD2HvbllptLgwADSEyPJSIoio08Uqb0jSOsdQf+4cL3GRyf5zCdkbYOdx17bxf7Tlbx433hGJsdYXZJSqgtCAm2fDgHdP6VlWV2jnfzSanJLqsg9W8XhMxfZlFfGe7tPf7qdCCTHhjGodwSp8RGk9o4gOTaM5Ngw+sWGEhehZy235RMBcKGmgcde28WOE+f5yR3XcPOIJKtLUkq5UGiQjZHJMVd8sausbeREWQ0nymsoONdye7yshg/2nKaqvqnNawQQG2xIP7aNfjFhJMWEkhAVQkJUCL0jQ0h03IYF+08vwqkAEJE5wK8AG7DMGPOTNs+L4/kvAJeAB40xu53Ztrs+yS/jP97aR3lNPb+6e+yn44pKKd8XExb0aW+hNWMMFy41UlxRy+mKWoodP3vzTnGxrokjJaWcq6pv9zUjQwJbgiEyhPjIYGLDg4gJa7mNDQsiJiyImPAgYi8vCw8iLMjmlTurOwwAEbEBS4CbgCJgh4isMMYcarXaXCDd8TMJeB6Y5OS2nWaMYfepCy2XtDtcSlrvCJY9ME2HfZRSQMvlL+MigomLCP6nz4Xs7FKysqYB0Ghv5nxNA+eq6lt+qus/vV/muJ9XWk1lbSOVlxo/3THdnsAAISIkkMiQQCJCbJ/dDw4k4oplNsKDAwkJCiAk0EZoUAChQTZCg2yEBF6+H0BooI0Qx627zqZ2pgcwEcg3xhQAiMhyYB7Q+kN8HvBHY4wBtopIrIj0BVKd2PYKzQbOVNbS2GRosDdT32Sn9GI9pytqOXi6ks3Hyig8X0tUaCDfmJ3Bw9MG+VW3TSnVfUG2APpEh9InuuM5wowx1DbaqbjUSGVto+O2gYpLjVTUtiy7VN9Edb2dmvomahqaqK5v4uzFOmrq7VTXN1FT30RTc9cuuRlsCyAkKIBgWwCBNiHIFkCQLYDAACHQFkCwrWsB4UwAJAOFrR4X0fItv6N1kp3c9gqnqpqZ8uP17T4XHRrIhNQ4nrpxKHNGJhGpR/oopdxMRAgPDiQ8OJB+sWFdeg1jDPVNzdTUN1HbaKeusZm6Rjv1Tc3UN9qpa2pZVt/0z8/VtVq30d5Mk93QaG+msdnQZG+m0W5oau7abKzOfHq2Fy1tY+zz1nFm25YXEFkALACISuzPQyOCsQVAoAi2AIgNEeJChV6hQoDUQFU+O7fkO1G+Z6muriY7O9vqMtxG2+fdtH3WCQDCHT//JNDx00HuvNqF93QmAIqA/q0epwDFTq4T7MS2ABhjlgJLATIyMsx359/kRGneJzs7m6ysLKvLcBttn3fT9vkXZ06n2wGki8ggEQkG7gZWtFlnBXC/tJgMVBpjzji5rVJKKQt02AMwxjSJyBPAGloO5XzZGJMjIgsdz78ArKLlENB8Wg4Dfehq27qlJUoppTrFqT2oxphVtHzIt172Qqv7Bnjc2W2VUkpZT2dUUkopP6UBoJRSfkoDQCml/JQGgFJK+SkNAKWU8lPScgCPZxGRKiDX6jrcpDdQZnURbqTt827aPu+VYYyJ6swGnjqRTq4xZoLVRbiDiOz01baBts/bafu8l4js7Ow2OgSklFJ+SgNAKaX8lKcGwFKrC3AjX24baPu8nbbPe3W6bR65E1gppZT7eWoPQCmllJtpACillJ/yqAAQkTkikisi+SKy2Op6uktEXhaRUhE52GpZnIisE5E8x20vK2vsDhHpLyIbROSwiOSIyFOO5V7fRhEJFZHtIrLP0bbvO5Z7fdtaExGbiOwRkb86HvtM+0TkhIgcEJG9lw+R9LH2xYrIOyJyxPE3OKWz7fOYABARG7AEmAtkAveISKa1VXXbH4A5bZYtBj4yxqQDHzkee6sm4D+NMcOBycDjjt+ZL7SxHrjBGDMaGAPMcVzsyBfa1tpTwOFWj32tfTONMWNaHfvvS+37FbDaGDMMGE3L77Fz7TPGeMQPMAVY0+rxt4BvWV2XC9qVChxs9TgX6Ou435eWk94sr9NFbf0LcJOvtZGWy7TuBib5UttouUTrR8ANwF8dy3ypfSeA3m2W+UT7gGjgOI4DebraPo/pAQDJQGGrx0WOZb6mj2m5XCaO20SL63EJEUkFxgLb8JE2OoZH9gKlwDpjjM+0zeGXwNNAc6tlvtQ+A6wVkV0issCxzFfalwacA15xDOEtE5EIOtk+TwoAaWeZHqPqBUQkEngXWGSMuWh1Pa5ijLEbY8bQ8k15ooiMtLgklxGRW4FSY8wuq2txo2nGmHG0DCs/LiLXW12QCwUC44DnjTFjgRq6MJzlSQFQBPRv9TgFKLaoFnc6KyJ9ARy3pRbX0y0iEkTLh//rxpj3HIt9qo3GmAogm5b9Ob7StmnA7SJyAlgO3CAir+E77cMYU+y4LQXeBybiO+0rAoocvVKAd2gJhE61z5MCYAeQLiKDRCQYuBtYYXFN7rACeMBx/wFaxs29kogI8BJw2Bjz81ZPeX0bRSRBRGId98OAWcARfKBtAMaYbxljUowxqbT8ra03xtyHj7RPRCJEJOryfeBm4CA+0j5jTAlQKCIZjkU3AofobPus3pnRZgfGF4CjwDHg21bX44L2vAGcARppSexHgHhadrzlOW7jrK6zG+2bTssw3X5gr+PnC77QRmAUsMfRtoPAs47lXt+2dtqaxWc7gX2ifbSMke9z/ORc/jzxlfY52jIG2On4P/oB0Kuz7dOpIJRSyk950hCQUkqpHqQBoJRSfkoDQCml/JQGgFJK+SkNAKWU8lMaAEop5ac0AJRSyk/9f6bPkkKm48vSAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Rl = linspace(1e-6,100,1000)\n", "l,En=3,-1/4**2\n", "f = fSchrod(En,l,Rl[::-1]) # here we turn mesh R around, so that f is given from large r down to r=0.\n", "ur = Numerovc(f,0.0,1e-7,Rl[1]-Rl[0])[::-1] # turn around the solution, so that it starts with r=0\n", "norm = integrate.simps(ur**2,x=Rl)\n", "ur *= 1/sqrt(abs(norm))\n", "\n", "plot(Rl,ur,'-')\n", "xlim(0,60)\n", "grid()" ] }, { "cell_type": "code", "execution_count": 127, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Rl = linspace(1e-6,100,1000)\n", "l,En=1,-1/3**2 # 3p orbital\n", "\n", "\n", "f = fSchrod(En,l,Rl[::-1])\n", "ur = Numerovc(f,0.0,-1e-7,-Rl[1]+Rl[0])[::-1]\n", "norm = integrate.simps(ur**2,x=Rl)\n", "ur *= 1/sqrt(abs(norm))\n", "\n", "plot(Rl,ur, label='u(r)')\n", "plot(Rl,ur/Rl, label='u(r)/r')\n", "legend(loc='best')\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Put it all together" ] }, { "cell_type": "code", "execution_count": 128, "metadata": {}, "outputs": [], "source": [ "def fSchrod(En, l, R):\n", " return l*(l+1.)/R**2-2./R-En\n", "\n", "def ComputeSchrod(En,R,l):\n", " \"Computes Schrod Eq.\" \n", " f = fSchrod(En,l,R[::-1])\n", " ur = Numerovc(f,0.0,-1e-7,-R[1]+R[0])[::-1]\n", " norm = integrate.simps(ur**2,x=R)\n", " return ur*1/sqrt(abs(norm))\n", "\n", "def Shoot(En,R,l):\n", " ur = ComputeSchrod(En,R,l)\n", " ur = ur/R**l\n", " f0,f1 = ur[0],ur[1]\n", " f_at_0 = f0 + (f1-f0)*(0.0-R[0])/(R[1]-R[0])\n", " return f_at_0\n", "\n", "def FindBoundStates(R,l,nmax,Esearch):\n", " n=0\n", " Ebnd=[]\n", " u0 = Shoot(Esearch[0],R,l)\n", " for i in range(1,len(Esearch)):\n", " u1 = Shoot(Esearch[i],R,l)\n", " if u0*u1<0:\n", " Ebound = optimize.brentq(Shoot,Esearch[i-1],Esearch[i],xtol=1e-16,args=(R,l))\n", " #Ebound = optimize.toms748(Shoot,Esearch[i-1],Esearch[i],xtol=1e-16,rtol=3.e-16,args=(R,l))\n", " Ebnd.append((l,Ebound))\n", " if len(Ebnd)>nmax: break\n", " n+=1\n", " print('Found bound state at E=%14.9f E_exact=%14.9f l=%d' % (Ebound, -1.0/(n+l)**2,l))\n", " u0=u1\n", " return Ebnd\n", "\n", "def cmpKey(x):\n", " return x[1] + x[0]/1000. # energy has large wait, but degenerate energy states are sorted by l\n" ] }, { "cell_type": "code", "execution_count": 129, "metadata": {}, "outputs": [], "source": [ "def ChargeDensity(Bnd,R,Z):\n", " rho = zeros(len(R))\n", " N=0.\n", " for (l,En) in Bnd:\n", " ur = ComputeSchrod(En, R, l)\n", " dN = 2*(2*l+1)\n", " if N+dN <= Z:\n", " ferm = 1.\n", " else:\n", " ferm = (Z-N)/float(dN)\n", " drho = ur**2 * ferm * dN/(4*pi*R**2) # contribution to density per unit volume\n", " rho += drho\n", " N += dN\n", " print('adding state', (l,En), 'with fermi=', ferm)\n", " if N>=Z: break\n", " return rho" ] }, { "cell_type": "code", "execution_count": 137, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Found bound state at E= -0.999921923 E_exact= -1.000000000 l=0\n", "Found bound state at E= -0.249990167 E_exact= -0.250000000 l=0\n", "Found bound state at E= -0.111108194 E_exact= -0.111111111 l=0\n", "Found bound state at E= -0.062498769 E_exact= -0.062500000 l=0\n", "Found bound state at E= -0.039999312 E_exact= -0.040000000 l=0\n", "Found bound state at E= -0.250000016 E_exact= -0.250000000 l=1\n", "Found bound state at E= -0.111111117 E_exact= -0.111111111 l=1\n", "Found bound state at E= -0.062500003 E_exact= -0.062500000 l=1\n", "Found bound state at E= -0.039999959 E_exact= -0.040000000 l=1\n", "Found bound state at E= -0.111111111 E_exact= -0.111111111 l=2\n", "Found bound state at E= -0.062500000 E_exact= -0.062500000 l=2\n", "Found bound state at E= -0.039999977 E_exact= -0.040000000 l=2\n", "Found bound state at E= -0.062500000 E_exact= -0.062500000 l=3\n", "Found bound state at E= -0.039999992 E_exact= -0.040000000 l=3\n", "adding state (0, -0.9999219225299896) with fermi= 1.0\n", "adding state (0, -0.24999016675537122) with fermi= 1.0\n", "adding state (1, -0.250000015612501) with fermi= 1.0\n", "adding state (0, -0.11110819386632778) with fermi= 1.0\n", "adding state (1, -0.11111111678120283) with fermi= 1.0\n", "adding state (2, -0.11111111114690181) with fermi= 1.0\n", "adding state (0, -0.06249876875886757) with fermi= 1.0\n", "adding state (1, -0.0625000025587252) with fermi= 1.0\n", "adding state (2, -0.06250000002526974) with fermi= 1.0\n", "adding state (3, -0.06250000000087207) with fermi= 1.0\n", "adding state (0, -0.03999931247010381) with fermi= 1.0\n", "adding state (1, -0.03999995861216955) with fermi= 1.0\n", "adding state (2, -0.039999976852458194) with fermi= 1.0\n", "adding state (3, -0.039999991776960016) with fermi= 1.0\n", "adding state (0, -0.027736582871674794) with fermi= 1.0\n", "adding state (1, -0.02774363595791085) with fermi= 1.0\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Esearch = -1.2/arange(1,20,0.2)**2\n", "R = linspace(1e-6,100,2000)\n", "\n", "nmax=5\n", "Bnd=[]\n", "for l in range(nmax-1):\n", " Bnd += FindBoundStates(R,l,nmax-l,Esearch)\n", "Bnd = sorted(Bnd, key=cmpKey)\n", "\n", "Z=100 # Like Ni ion\n", "\n", "rho = ChargeDensity(Bnd,R,Z)\n", "\n", "plot(R,rho*(4*pi*R**2),label='charge density')\n", "xlim([0,80])\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It seems with Numerov we are getting substantial error-bar for the energy of 1s state. We could increase the number of points in the mesh, but the error decreases only linearly with the number of points used.\n", "\n", "Where is the problem? What should be done?" ] }, { "cell_type": "code", "execution_count": 143, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.9999219225299939" ] }, "execution_count": 143, "metadata": {}, "output_type": "execute_result" } ], "source": [ "optimize.brentq(Shoot,-1.1,-0.99,xtol=1e-16,args=(R,0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check that approximate solution gives smaller wave function at zero than exact energy, which confirms that root finding routine works fine." ] }, { "cell_type": "code", "execution_count": 144, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(9.742600661365844e-08, 2.3262457545341758e-10)" ] }, "execution_count": 144, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Shoot(-1.0,R,l=0), Shoot(-0.9999221089559636,R,l=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's check how the function looks like near zero" ] }, { "cell_type": "code", "execution_count": 145, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 0.4)" ] }, "execution_count": 145, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ur = ComputeSchrod(-1.0,R,0)\n", "plot(R,ur,'o-')\n", "xlim(0,0.2)\n", "ylim(0,0.4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Idea: The mesh is very sparse near zero, and in the range of the first few points, the curve is not linear enough. Linear extrapolation gives the error.\n", "\n", "Can we do better?\n", "\n", "Let's use cubic extrapolation with first 4 points." ] }, { "cell_type": "code", "execution_count": 146, "metadata": {}, "outputs": [], "source": [ "def Shoot2(En,R,l):\n", " ur = ComputeSchrod(En,R,l)\n", " ur = ur/R**l\n", " poly = polyfit(R[:4], ur[:4], deg=3)\n", " return polyval(poly, 0.0)" ] }, { "cell_type": "code", "execution_count": 147, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(7.080962919685301e-11, -9.638466798368069e-08)" ] }, "execution_count": 147, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Shoot2(-1,R,l=0), Shoot2(-0.9999221089559636,R,l=0)" ] }, { "cell_type": "code", "execution_count": 150, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.9999999428188622" ] }, "execution_count": 150, "metadata": {}, "output_type": "execute_result" } ], "source": [ "optimize.brentq(Shoot2,-1.1,-0.9,xtol=1e-16,args=(R,0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indeed we get $10^{-8}$ error as compared to $10^{-5}$ error before.\n", "So, the extrapolation must be improved to reduce the error." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Increasing the number of points for 10-times reduces the error factor of 1000, i.e., $O(1/N^3)$.\n", "\n", "Better cubic extrapolation reduces the error for the same factor of 1000, equivalent to 10-times more points." ] }, { "cell_type": "code", "execution_count": 152, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Error with linear extrapolation: 7.80774700104292e-05\n", "Error with cubic extrapolation: 5.7181137824713346e-08\n" ] } ], "source": [ "R = linspace(1e-6,100,2000)\n", "print('Error with linear extrapolation:', optimize.brentq(Shoot,-1.1,-0.9,xtol=1e-16,args=(R,0)) + 1.0 )\n", "print('Error with cubic extrapolation:', optimize.brentq(Shoot2,-1.1,-0.9,xtol=1e-16,args=(R,0)) + 1.0 )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It also helps to increase the number of points. 10-times denser grid gives roughly $10^{-3}$ smaller error." ] }, { "cell_type": "code", "execution_count": 153, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Error with linear extrapolation: 8.297734188644768e-08\n", "Error with cubic extrapolation: -1.092637091915094e-11\n" ] } ], "source": [ "R = linspace(1e-8,100,20000)\n", "print('Error with linear extrapolation:', optimize.brentq(Shoot,-1.1,-0.9,xtol=1e-16,args=(R,0)) + 1.0 )\n", "print('Error with cubic extrapolation:', optimize.brentq(Shoot2,-1.1,-0.9,xtol=1e-16,args=(R,0)) + 1.0 )" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }