This document describes how, given an initial wave function, the wave
function at time t can be found. First the initial wave function is
decomposed into an expansion of the Hamiltonian eigenfunctions. Time
dependence is then applied to these eigenfunctions. Finally, the wave
function in x-space is recreated from the expansion.
A free particle gaussian wave packet is used as an example. All
calculations are done discretely, such that they may readily be
implemented in Matlab .