{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Numerical methods for the Schrodinger equation\n", "\n", "##### by Justin Cai and Sam Bateman" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from tise_code import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving the time-independent Schrodinger equation\n", "\n", "Recall the that time-independent Schrodinger equation (TISE) is \n", "\n", "$$-\\frac{\\hbar^2}{2m}\\frac{d^2\\psi}{dx^2} + V \\psi = E\\psi.$$\n", "\n", "When solving the time-independet Schrodinger equation (TISE), we are faced with solving a boundary value problem (BVP), or finding a solution to a differential equation with the solution being specified at two or more points. This is contrasted with an initial value problem (IVP), where we want to find a solution with the solution only specified at one point. For the TISE, if we restrict our particle to the finite domain $[a, b]$, then we'll have that $\\psi(a)=0=\\psi(b)$ as our boundary conditions.\n", "\n", "### Shooting method\n", "\n", "One method to solving boundary value problems is called the shooting method. The shooting method turns the problem into an initial value problem by starting at one of the boundaries, guessing an initial free parameter, solving up to the boundary (that is, \"shooting\" to the boundary), and checking if our solution matches the boundary condition. If it does not, we update our guess on our free parameter and then repeat this process until our solution is sufficiently close to the boundary condition.\n", "\n", "Let's see this in a simple scenario with an infinite square well. Recall that the potential of an infinite square is \n", "\n", "$$V(x) = \\begin{cases}0 & 0 \\leq x \\leq L \\\\ \\infty & \\text{otherwise} \\end{cases},$$\n", "\n", "so we get the boundary conditions $\\psi(0)=0=\\psi(L)$ discussed earlier. We'll have to make a guess for the initial slope, so turning this into an IVP, we have $\\psi(0)=0, \\psi'(0)=s$, where $s$ is a free parameter. For arbitrary potentials, we also don't know $E$, the total energy of the system, but for now, we'll plug in the analytic solution for the energy of an infinite square well,\n", "\n", "$$E_n = \\frac{n^2 \\pi^2 \\hbar^2}{2mL^2}.$$\n", "\n", "For convenience, we'll also set $m=1$ and $h=1$ (so $\\hbar = \\frac{1}{2\\pi}$). If we solve this IVP with the correct energy, then we see that the initial slope doesn't really matter:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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