Numerical Solution of 1D Time Independent Schrodinger Equation using Finite Difference Method.

Finite Difference scheme is applied to Time Independent Schrodinger Equation.

In this code, a potential well is taken (particle in a box) and the wave-function of the particle is calculated by solving Schrodinger equation. Finite difference method is used. Energy must be prescribed before calculating wave-function. Also constants like mass, Planck's constant and length of potential well are all normalized to unity for simplicity. At the end, wave-function is normalized to get probability density function using MATLAB inbuilt trapz command (trapezoidal rule) for numerical integration. Finally for visualizing, some array manipulation is done. For four different energy level, wave-function (or the probability density function) is plotted at the end.