eigenenergy, eigenstate, schrödinger equation, tunneling, scattering, ehrenfest's theorem, animation

The Time-Dependent Schrödinger equation is solved by expressing the solution as a linear combination of (stationary) solutions of the Time-Independent Schrödinger equation.

animation, schrödinger equation, tunneling, scattering

A one-dimensional wave-packet is propagated forward in time for various different potentials.

The eigenenergies of a system are found by discretizing the Schrödinger equation and finding the eigenvalues of the resulting matrix.

eigenenergy, forward shooting, eigenstate, schrödinger equation

Using a forward-shooting method to determine the eigenenergies and eigenfunctions of an asymmetric potential in one dimension.

Employing Monte Carlo integration to determine the "shape" of the hydrogen molecule ion.

schrödinger equation, bloch's theorem, newton's theorem

Using Newton's method to calculate the band structure for the simple Dirac comb potential in one dimension.