{ "cells": [ { "attachments": { "Griffiths-Pr-1.7.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "fc820d80", "metadata": {}, "source": [ "![Griffiths-Pr-1.7.png](attachment:Griffiths-Pr-1.7.png)" ] }, { "cell_type": "markdown", "id": "2f578d68", "metadata": {}, "source": [ "I presume this is based on equation 1.35 of Griffiths book." ] }, { "attachments": { "Griffiths-Eq-1.35.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "8f4aa4f9", "metadata": {}, "source": [ "![Griffiths-Eq-1.35.png](attachment:Griffiths-Eq-1.35.png)" ] }, { "cell_type": "code", "execution_count": 14, "id": "d906f110", "metadata": {}, "outputs": [], "source": [ "import sympy as sp\n", "from sympy import I\n", "sp.init_printing()" ] }, { "cell_type": "markdown", "id": "ce9127ea", "metadata": {}, "source": [ "The above looks a bit tricky to work out but the only formula I know that makes a direct reference to potential is Schrödinger's equation.\n", "\n", "$$ i \\hbar \\frac{\\partial }{\\partial t} \\Psi (x,t) = \\left [ \\frac{- \\hbar^2}{2m} \\frac{\\partial}{\\partial x^2} + V(x) \\right ] \\Psi (x,t) $$" ] }, { "cell_type": "code", "execution_count": 6, "id": "4566d215", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left( \\hbar, \\ m\\right)$" ], "text/plain": [ "(h̅, m)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hbar, m = sp.symbols('hbar m', real=True, positive=True)\n", "hbar, m" ] }, { "cell_type": "code", "execution_count": 20, "id": "45109a03", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left( x, \\ t, \\ E\\right)$" ], "text/plain": [ "(x, t, E)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x, t, E = sp.symbols(\"x t E\", real=True)\n", "x,t,E" ] }, { "cell_type": "code", "execution_count": 49, "id": "7206cb25", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle Ψ{\\left(x,t \\right)}$" ], "text/plain": [ "Ψ(x, t)" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "psi = sp.Function(\"Ψ\")(x,t)\n", "psi" ] }, { "cell_type": "markdown", "id": "9e5b1a0d", "metadata": {}, "source": [ "We define s1 which we can use for $ \\frac{\\partial \\Psi}{ \\partial t} $ which we arrive at by just rearranging the Schrödinger equation" ] }, { "cell_type": "code", "execution_count": 50, "id": "18a72c0d", "metadata": {}, "outputs": [ { "data": { "image/png": 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EVhr+D0rEyorytVdIAAAAAElFTkSuQmCC\n", "text/latex": [ "$\\displaystyle i \\hbar \\frac{\\partial}{\\partial t} Ψ{\\left(x,t \\right)} = - \\frac{\\hbar^{2} \\frac{\\partial^{2}}{\\partial x^{2}} Ψ{\\left(x,t \\right)}}{2 m} + V{\\left(x \\right)} Ψ{\\left(x,t \\right)}$" ], "text/plain": [ " 2 \n", " 2 ∂ \n", " h̅ ⋅───(Ψ(x, t)) \n", " 2 \n", " ∂ ∂x \n", "ⅈ⋅h̅⋅──(Ψ(x, t)) = - ─────────────── + V(x)⋅Ψ(x, t)\n", " ∂t 2⋅m " ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s1 = sp.Eq(I*hbar*psi.diff(t), (-hbar**2/(2*m)*psi.diff(x,x) + v*psi))\n", "s1" ] }, { "cell_type": "code", "execution_count": 58, "id": "de718d5a", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{\\partial}{\\partial t} Ψ{\\left(x,t \\right)} = \\frac{i \\hbar \\frac{\\partial^{2}}{\\partial x^{2}} Ψ{\\left(x,t \\right)}}{2 m} - \\frac{i V{\\left(x \\right)} Ψ{\\left(x,t \\right)}}{\\hbar}$" ], "text/plain": [ " 2 \n", " ∂ \n", " ⅈ⋅h̅⋅───(Ψ(x, t)) \n", " 2 \n", "∂ ∂x ⅈ⋅V(x)⋅Ψ(x, t)\n", "──(Ψ(x, t)) = ──────────────── - ──────────────\n", "∂t 2⋅m h̅ " ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s2 = sp.Eq((s1.lhs)/(I*hbar) , sp.simplify((s1.rhs)/(I*hbar)))\n", "s2" ] }, { "cell_type": "markdown", "id": "a9e2a056", "metadata": {}, "source": [ "Now we know that by the product rule ...\n", "$$ \\frac{d^2 \\Psi}{dx^2} = 2 \\Psi(x) * \\frac{ d \\Psi }{ dx } $$\n", "\n", "\n", "(I had to do a quick check here that the product rule applies equally for partial deriviatives which it does seem to.)\n", "\n", "Then integrating with respect to x yields ...\n", "\n", "$$ < p > = \\int \\overline{\\Psi} \\frac{\\hbar}{i} \\frac{ \\partial } { \\partial x } \\Psi dx \\\\ \n", "= \\frac{i}{2 \\hbar} \\int \\frac{ d( \\Psi^2 )}{dx} dx \\\\\n", "= \\frac{i}{2 \\hbar} \\left[ \\Psi (x,t) \\right] ^2 $$" ] }, { "cell_type": "code", "execution_count": 61, "id": "220895c2", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle - i \\hbar \\overline{Ψ{\\left(x,t \\right)}} \\frac{\\partial}{\\partial x} Ψ{\\left(x,t \\right)}$" ], "text/plain": [ " _______ ∂ \n", "-ⅈ⋅h̅⋅Ψ(x, t)⋅──(Ψ(x, t))\n", " ∂x " ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s3 = psi.conjugate()*(hbar/I)*psi.diff(x)\n", "s3" ] }, { "cell_type": "code", "execution_count": 63, "id": "830d8b5f", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle - i \\hbar \\overline{Ψ{\\left(x,t \\right)}} \\frac{\\partial^{2}}{\\partial x\\partial t} Ψ{\\left(x,t \\right)} - i \\hbar \\overline{\\frac{\\partial}{\\partial t} Ψ{\\left(x,t \\right)}} \\frac{\\partial}{\\partial x} Ψ{\\left(x,t \\right)}$" ], "text/plain": [ " 2 ___________ \n", " _______ ∂ ∂ ∂ \n", "- ⅈ⋅h̅⋅Ψ(x, t)⋅─────(Ψ(x, t)) - ⅈ⋅h̅⋅──(Ψ(x, t))⋅──(Ψ(x, t))\n", " ∂x ∂t ∂t ∂x " ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s3.diff(t)" ] }, { "cell_type": "code", "execution_count": null, "id": "562989e1", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }