{ "cells": [ { "cell_type": "markdown", "id": "57a3e0ba", "metadata": {}, "source": [ "# Computer Lab Semester - 5" ] }, { "cell_type": "markdown", "id": "04731fc4", "metadata": {}, "source": [ "## Problem - 1\n", "\n", "Solve the s-wave Schrödinger equation for the ground state and the first excited state of the hydrogen atom\n", "\\begin{align}\n", "&\\frac{d^2u}{dr^2}=A(r)u(r),\\\\\n", "&A(r) = \\frac{2m}{\\hbar^2}[V(r)-E],\\\\\n", "\\mbox{where, } &V(r)=-\\frac{e^2}{r}\n", "\\end{align}\n", "where, m is the reduced mass of the electron. Obtain the energy eigenvalues and plot the corresponding wave\n", "functions. Remember that the ground state energy of the hydrogen atom is ≈-13.6 eV. Take e=3.795 (eVÅ),\n", "ħc= 1973(eVÅ) and m=0.511×10$^6$ eV/c$^2$." ] }, { "cell_type": "markdown", "id": "4ff104df", "metadata": {}, "source": [ "## Time independent Scrodinger equation\n", "\\begin{equation}\n", "\\frac{d^2\\psi(x)}{dx^2} + k^2(x)\\psi(x) = 0\n", "\\end{equation}\n", "where,\n", "\\begin{equation}\n", "k^2(x)=\\frac{2m}{\\hbar^2}(E-V(x))\n", "\\end{equation}\n", "\n", "We split the second order differential equation into two first order equations as below -\n", "\\begin{equation}\n", "\\begin{aligned}\n", "&\\frac{d\\psi}{dx}=\\phi(x)\\\\\n", "&\\frac{d\\phi}{dx}=-k^2(x)\\psi(x)\n", "\\end{aligned}\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 1, "id": "07910b15", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import odeint\n", "from scipy.optimize import bisect" ] }, { "cell_type": "code", "execution_count": 2, "id": "12e23487", "metadata": {}, "outputs": [], "source": [ "# Basic parameters\n", "E0 = -13.6 # approximate ground state energy\n", "e = 3.795 # charge of electron in eVA\n", "hbarc = 1973 # in eVA\n", "m = 0.511e6 # in eV/c^2\n", "\n", "# Based on the given parameters, calculate 2m/hbar^2c\n", "C = 2*m/hbarc**2" ] }, { "cell_type": "code", "execution_count": 3, "id": "667e1830", "metadata": {}, "outputs": [], "source": [ "# Defining Helper Functions\n", "\n", "def V(r):\n", " return - e**2/r \n", "\n", "def A(r):\n", " return C*(V(r)-E)\n", "\n", "def dzdr(z, r):\n", " x, y = z\n", " dxdr = y\n", " dydr = A(r)*x\n", " dzdr = np.array([dxdr, dydr])\n", " return dzdr\n", "\n", "def waveFunc(energy):\n", " global sol\n", " global E\n", " E = energy\n", " sol = odeint(dzdr, z[0], r)\n", " return sol[-1, 0]\n" ] }, { "cell_type": "code", "execution_count": 13, "id": "1b78a774", "metadata": {}, "outputs": [], "source": [ "# setting arrays for storing values\n", "\n", "r = np.arange(1e-15, 8, 0.01)\n", "z = np.zeros([len(r),2])\n", "x0 = 0.001\n", "y0 = 1\n", "z[0] = [x0, y0]" ] }, { "cell_type": "code", "execution_count": 19, "id": "b26a10c3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Energy Eigen Values are \n", "[-13.7319, -3.4059, -0.7694]\n" ] } ], "source": [ "# Finding energy eigen values\n", "\n", "Energy = np.linspace(-20, 0, 100)\n", "waveFuncRight = np.array([waveFunc(Eval) for Eval in Energy])\n", "sign = np.sign(waveFuncRight)\n", "eigenValue = []\n", "for i in range(len(sign)-1):\n", " if sign[i] == - sign[i+1]:\n", " en = bisect(waveFunc, Energy[i], Energy[i+1])\n", " en = round(en,4)\n", " eigenValue += [en]\n", "\n", "print('Energy Eigen Values are \\n'+str(eigenValue))" ] }, { "cell_type": "code", "execution_count": 20, "id": "67e16dc7", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plotting wavefunctions\n", "\n", "def plot():\n", " fig, ax = plt.subplots(figsize=(8, 5))\n", " # set the x-spine\n", " ax.spines['left'].set_position('zero')\n", "\n", " # turn off the right spine/ticks\n", " ax.spines['right'].set_color('none')\n", " ax.yaxis.tick_left()\n", "\n", " # set the y-spine\n", " ax.spines['bottom'].set_position('zero')\n", "\n", " # turn off the top spine/ticks\n", " ax.spines['top'].set_color('none')\n", " ax.xaxis.tick_bottom()\n", "\n", "plot()\n", "\n", "color = ['red', 'blue', 'orange']\n", "for i in range(len(eigenValue)):\n", " waveFunc(eigenValue[i])\n", " plt.plot(r, sol[:,0], color=color[i], label='n = '+str(i)+' E'+str(i)+' = '+str(round(eigenValue[i],1)))\n", "\n", "plt.xlabel('r')\n", "plt.ylabel('$\\psi(r)$')\n", "plt.legend()\n", "#plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "267bbdb5", "metadata": {}, "source": [ "## Problem - 2\n", "\n", "Solve the s-wave radial Schrödinger equation for an atom\n", "\\begin{align}\n", "&\\frac{d^2y}{dr^2}=A(r)u(r),\\\\\n", "&A(r) = \\frac{2m}{\\hbar^2}[V(r)-E],\\\\\n", "\\mbox{where, } &V(r)=-\\frac{e^2}{r}\n", "\\end{align}\n", "Where m is the reduced mass of the system (which can be chosen to be the mass of an electron), for the screened Coulomb potential\n", "\\begin{align}\n", "V(r) = -\\frac{e^2}{r}e^{-r/a}\n", "\\end{align}\n", "Find the energy (in eV) of the ground state of the atom to an accuracy of three significant digits. Also, plot the corresponding wave function. Take e=3.795 (eVÅ), and a=3 Å, 5 Å, and 7 Å in the units of ħc = 1973(eVÅ) and m=0.511×10$^6$ eV/c$^2$. The ground state energy is expected to be above -12 eV in all\n", "three cases." ] }, { "cell_type": "code", "execution_count": 21, "id": "0139b20f", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import odeint\n", "from scipy.optimize import bisect" ] }, { "cell_type": "code", "execution_count": 22, "id": "880fd8a2", "metadata": {}, "outputs": [], "source": [ "# Basic parameters\n", "E0 = -12 # approximate ground state energy\n", "e = 3.795 # charge of electron in eVA\n", "hbarc = 1973 # in eVA\n", "m = 0.511e6 # in eV/c^2\n", "a = 5 # in units of angstrum\n", "\n", "# Based on the given parameters, calculate 2m/hbar^2c\n", "C = 2*m/hbarc**2" ] }, { "cell_type": "code", "execution_count": 23, "id": "048c9276", "metadata": {}, "outputs": [], "source": [ "# Defining Helper Functions\n", "\n", "def V(r):\n", " return - (e**2/r )*np.exp(-r/a)\n", "\n", "def A(r):\n", " return C*(V(r)-E)\n", "\n", "def dzdr(z, r):\n", " x, y = z\n", " dxdr = y\n", " dydr = A(r)*x\n", " dzdr = np.array([dxdr, dydr])\n", " return dzdr\n", "\n", "def waveFunc(energy):\n", " global sol\n", " global E\n", " E = energy\n", " sol = odeint(dzdr, z[0], r)\n", " return sol[-1, 0]" ] }, { "cell_type": "code", "execution_count": 24, "id": "6f520310", "metadata": {}, "outputs": [], "source": [ "# setting arrays for storing values\n", "\n", "r = np.arange(1e-15, 10, 0.01)\n", "z = np.zeros([len(r),2])\n", "x0 = 0.001\n", "y0 = 1\n", "z[0] = [x0, y0]" ] }, { "cell_type": "code", "execution_count": 25, "id": "703b0904", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Energy Eigen Values are \n", "[-11.06410939502324, -1.284295766697573]\n" ] } ], "source": [ "# Finding energy eigen values\n", "\n", "Energy = np.linspace(-20, 0, 100)\n", "waveFuncRight = np.array([waveFunc(Eval) for Eval in Energy])\n", "sign = np.sign(waveFuncRight)\n", "eigenValue = []\n", "for i in range(len(sign)-1):\n", " if sign[i] == - sign[i+1]:\n", " en = bisect(waveFunc, Energy[i], Energy[i+1])\n", " eigenValue += [en]\n", "\n", "print('Energy Eigen Values are \\n'+str(eigenValue))" ] }, { "cell_type": "code", "execution_count": 26, "id": "93763320", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plotting wavefunctions\n", "\n", "def plot():\n", " fig, ax = plt.subplots(figsize=(8, 5))\n", " # set the x-spine\n", " ax.spines['left'].set_position('zero')\n", "\n", " # turn off the right spine/ticks\n", " ax.spines['right'].set_color('none')\n", " ax.yaxis.tick_left()\n", "\n", " # set the y-spine\n", " ax.spines['bottom'].set_position('zero')\n", "\n", " # turn off the top spine/ticks\n", " ax.spines['top'].set_color('none')\n", " ax.xaxis.tick_bottom()\n", "\n", "plot()\n", "\n", "color = ['red', 'blue', 'orange']\n", "for i in range(len(eigenValue)):\n", " waveFunc(eigenValue[i])\n", " plt.plot(r, sol[:,0], color=color[i], label='n = '+str(i)+' E'+str(i)+' = '+str(round(eigenValue[i],1)))\n", "\n", "plt.xlabel('r')\n", "plt.ylabel('$\\psi(r)$')\n", "plt.text(8,0.08, '$V(r)=\\\\frac{e^2}{r}e^{-r/a}; \\\\ a$ = '+str(a))\n", "plt.legend()\n", "#plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "ea1d10e4", "metadata": {}, "source": [ "## Problem 3\n", "\n", "Solve the s-wave Schrodinger equation for the ground state and the first excited state of the hydrogen atom\n", "\\begin{equation}\n", "\\frac{d^2y}{dr^2}=A(r)u(r),\\hspace{1cm}A(r)=\\frac{2m}{\\hbar^2}[V(r) - E]\\mbox{~where~}V(r)=-\\frac{e^2}{r}\n", "\\end{equation}\n", "The anharmonic potential\n", "\\begin{equation}\n", "V(r)=\\frac{1}{2}kr^2 + \\frac{1}{3}br^3\n", "\\end{equation}\n", "for the ground state energy (in MeV) of particle to an accuracy of three significant digits. Also, plot the corressponding wave function. Choose $m=940 MeV/c^2$, $k=100 MeVfm^{-2}$, $b=0,10,30 MeVfm^{-3}$. In these units, $c\\hbar=940 MeV/c^2$, $k=100 MeVfm^{-3}$ for all three cases. The ground state energy is expected to lie in between 90 and 110 MeV for all three cases." ] }, { "cell_type": "code", "execution_count": 34, "id": "a441fe13", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import odeint\n", "from scipy.optimize import newton, bisect, brentq\n", "from scipy.constants import hbar, m_e" ] }, { "cell_type": "code", "execution_count": 35, "id": "09f5a6f5", "metadata": {}, "outputs": [], "source": [ "# Defining helper functions\n", "\n", "# (1) Potential function\n", "\n", "def V(r):\n", " V = (1/2)*k*r**2 + (1/3)*b*r**3\n", " return V\n", "\n", "# (2) Defining A(r)\n", "\n", "def A(r):\n", " a = (2*m_e/ħc**2)*(V(r) - E)\n", " return a\n", "\n", "# (3) Defining Derivative functions of 'y'\n", "\n", "def deriv(y, r):\n", " return np.array([y[1], A(r)*y[0]])\n", "\n", "# (4) Defining wave function with respect to energy\n", "\n", "def waveFunc(energy):\n", " global E\n", " global psi\n", " E = energy\n", " psi = odeint(deriv, psi0, r)\n", " return psi[-1, 0]\n", "\n", "# (5) Finding zero of the wavefuncton by Shooting method\n", "\n", "def zero(x, y):\n", " energyEigenValue = []\n", " s = np.sign(y)\n", " #s = np.array(s, dtype=int)\n", " for i in range(len(s)-1):\n", " if s[i] == -s[i+1]:\n", " zero = bisect(waveFunc, x[i], x[i+1])\n", " energyEigenValue.append(zero)\n", " return energyEigenValue\n", "\n", "# Vectorizing the functions\n", "V = np.vectorize(V)\n", "waveFunc = np.vectorize(waveFunc)\n", "zero = np.vectorize(zero)" ] }, { "cell_type": "code", "execution_count": 42, "id": "4474f16b", "metadata": {}, "outputs": [], "source": [ "# Important parameters\n", "\n", "m_e = 940\n", "ħc = 197.3\n", "k = 100\n", "# Initialisation\n", "\n", "N = 1000 # Number of points on x-axis\n", "psi = np.zeros([N, 2]) # To store wave function values and its derivative\n", "psi0 = np.array([0.001, 0]) # wavefunction of initial staes\n", "\n", "b = 30\n", "r = np.linspace(-3, 3, N) # x - axis" ] }, { "cell_type": "code", "execution_count": 43, "id": "d852b617", "metadata": {}, "outputs": [], "source": [ "En = np.arange(0, 150, 1)\n", "psiRight = waveFunc(En)\n", "#psiRight" ] }, { "cell_type": "code", "execution_count": 44, "id": "5600d620", "metadata": {}, "outputs": [], "source": [ "def zero(x, psi):\n", " energyEigenValue = []\n", " s = np.sign(psi)\n", " #s = np.array(s, dtype=int)\n", " for i in range(len(s)-1):\n", " if s[i] == -s[i+1]:\n", " zero = bisect(waveFunc, x[i], x[i+1])\n", " energyEigenValue.append(zero)\n", " return energyEigenValue" ] }, { "cell_type": "code", "execution_count": 45, "id": "0120e0c8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 31.55704024, 92.01776957, 144.81662013])" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "EigenValue = np.array(zero(En, psiRight))\n", "EigenValue" ] }, { "cell_type": "code", "execution_count": 46, "id": "d01311f0", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(5, 10))\n", "fig.subplots_adjust(hspace=0.4, wspace=0.4)\n", "j=1\n", "for i in range(len(EigenValue)):\n", " ax = fig.add_subplot(len(EigenValue), 1, j)\n", " waveFunc(EigenValue[i])\n", " plt.plot(r, psi.transpose()[0])\n", " ax.spines['left'].set_position('zero')\n", " ax.spines['right'].set_color('none')\n", " ax.spines['top'].set_color('none')\n", " ax.spines['bottom'].set_position('zero')\n", " #plt.legend()\n", " plt.xlabel('$r$', fontsize=14)\n", " plt.ylabel('$\\psi(r)$', fontsize=14)\n", " j+=1\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "ce9d12b8", "metadata": {}, "source": [ "## Problem 4\n", "\n", "Solve the s-wave Schrodinger equation for the hydrogen molecule\n", "\\begin{equation}\n", "\\frac{d^2y}{dr^2}=A(r)u(r),\\hspace{1cm}A(r)=\\frac{2\\mu}{\\hbar^2}[V(r) - E]\n", "\\end{equation}\n", "where, $\\mu$ is the reduced mass of the two-atom system for the Morse potential. \n", "\\begin{equation}\n", "V(r)=D\\left(e^{-2\\alpha r^{\\prime}} - e^{-\\alpha r^{\\prime}}\\right),\\hspace{0.5cm}r^{\\prime}=\\frac{r - r_0}{r}\n", "\\end{equation}\n", "Find the lowest vibrational energy (in MeV) of the molecule to an accuracy of three significant digits. Also plot\n", "the corressponding wave function. Take $m=940\\times 10^6 eV/c^2$, $D=0.755501$, $\\alpha=1.44$ and $r_0=0.131349 \\overset{\\circ}{A}$" ] }, { "cell_type": "markdown", "id": "e15307c6", "metadata": {}, "source": [ "Morse potential expression given is wrong. The correct form is\n", "\\begin{align}\n", "V(r) &= D \\left[1 - e^{-\\alpha(r-r_0)}\\right]^2\\\\\n", "V(r) &=D\\left(1 - 2e^{-\\alpha r^{\\prime}} + e^{-2\\alpha r^{\\prime}}\\right), \\hspace{0.5cm} r^{\\prime}=\\frac{r - r_0}{r}\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 27, "id": "af788022", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import odeint\n", "from scipy.optimize import newton, bisect, brentq\n", "from scipy.constants import hbar, m_e" ] }, { "cell_type": "code", "execution_count": 28, "id": "2980804c", "metadata": {}, "outputs": [], "source": [ "# Defining helper functions\n", "\n", "# (1) Potential function\n", "\n", "def V(r, r0, α, D):\n", " V = D*(1 - np.exp(-α*(r - r0)))**2\n", " return V\n", " \n", "# (2) Defining A(r)\n", "\n", "def A(r):\n", " a = (2*μ/ħc**2)*(V(r, r0, α, D) - E)\n", " return a\n", "\n", "# (3) Defining Derivative functions of 'y'\n", "\n", "def deriv(y, r):\n", " return np.array([y[1], A(r)*y[0]])\n", "\n", "# (4) Defining wave function with respect to energy\n", "\n", "def waveFunc(energy):\n", " global E\n", " global psi\n", " E = energy\n", " psi = odeint(deriv, psi0, r)\n", " return psi[-1, 0]\n", "\n", "# (5) Finding zero of the wavefuncton by Shooting method\n", "\n", "def zero(x, y):\n", " energyEigenValue = []\n", " s = np.sign(y)\n", " #s = np.array(s, dtype=int)\n", " for i in range(len(s)-1):\n", " if s[i] == -s[i+1]:\n", " zero = bisect(waveFunc, x[i], x[i+1])\n", " energyEigenValue.append(zero)\n", " return energyEigenValue\n", "\n", "# Vectorizing the functions\n", "V = np.vectorize(V)\n", "waveFunc = np.vectorize(waveFunc)\n", "zero = np.vectorize(zero)" ] }, { "cell_type": "code", "execution_count": 29, "id": "64ca7e39", "metadata": {}, "outputs": [], "source": [ "# Important parameters\n", "\n", "μ = 940e6\n", "D = 0.755501\n", "α = 1.44\n", "r0 = 0.131349\n", "ħc = 1973\n", "\n", "# Initialisation\n", "\n", "N = 100 # Number of points on x-axis\n", "psi = np.zeros([N, 2]) # To store wave function values and its derivative\n", "psi0 = np.array([0.001, 2]) # wavefunction of initial staes\n", "\n", "\n", "r = np.linspace(-0.2, 0.2, 100) # x - axis" ] }, { "cell_type": "code", "execution_count": 30, "id": "2cd67162", "metadata": {}, "outputs": [], "source": [ "En = np.arange(0, 15, 1)\n", "psiRight = waveFunc(En)\n", "#psiRight" ] }, { "cell_type": "code", "execution_count": 31, "id": "6264d76f", "metadata": {}, "outputs": [], "source": [ "def zero(x, psi):\n", " energyEigenValue = []\n", " s = np.sign(psi)\n", " #s = np.array(s, dtype=int)\n", " for i in range(len(s)-1):\n", " if s[i] == -s[i+1]:\n", " zero = bisect(waveFunc, x[i], x[i+1])\n", " energyEigenValue.append(zero)\n", " return energyEigenValue" ] }, { "cell_type": "code", "execution_count": 32, "id": "7b0b4a89", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1.21457505, 2.10732938, 3.2543345 , 4.65597459, 6.31235437,\n", " 8.22351125, 10.389463 , 12.81021612])" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "EigenValue = np.array(zero(En, psiRight))\n", "EigenValue" ] }, { "cell_type": "code", "execution_count": 33, "id": "fb21d2e5", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(5, 15))\n", "fig.subplots_adjust(hspace=0.4, wspace=0.4)\n", "j=1\n", "for i in range(len(EigenValue)):\n", " ax = fig.add_subplot(len(EigenValue), 1, j)\n", " waveFunc(EigenValue[i])\n", " plt.plot(r, psi.transpose()[0])\n", " #plt.legend()\n", " plt.xlabel('$r$', fontsize=14)\n", " plt.ylabel('$\\psi(r)$', fontsize=14)\n", " j+=1\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "2fbe6e19", "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": "3.7.6" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 5 }