The document describes numerically solving the time-independent Schrödinger equation for a particle in a one-dimensional potential well using finite differences. It involves discretizing the wavefunction and potential on a grid, then replacing derivatives with finite differences to form a matrix equation. The method is applied to find the first four energy eigenvalues and eigenfunctions of an electron in a 10nm rectangular potential well. Plots of the wavefunctions and probability densities are generated. The probability of finding the electron between 0.25-0.75nm for the ground state is calculated to be 0.05.