# Numerical solution of SE

1. Jun 20, 2011

### eoghan

Hi there!
I have to numerically solve the Schroedinger equation for a particle in a static magnetic field. Until now I've used the split operator technique using the Fourier transform. The problem is that this technique requires that the hamiltonian operator can be decoupled as:
$$H(\vec x, \vec p)=H_1(\vec x)+H_2(\vec p)$$
and so I can split it in two parts which are diagonal in the coordinate representation and in the momentum representation respectively.
The problem with a magnetic field is that the hamiltonian contains a term:
$$(p_x+By)^2$$
and so it can't be split.
So, what technique can I use to numerically solve the Schroedinger equation?
The website "Visual Quantum Mechanics" (http://www.kfunigraz.ac.at/imawww/vqm/movies.html [Broken])
says:
"A Gaussian wave function exp(-x^2/2) corresponds to a particle at rest if there is no external field. Did you know that in a constant magnetic field this wave packet describes a moving particle? The center of the wave packet moves on a circle which goes precisely through the origin (assuming that the vector potential is given in the Poincaré gauge)."
What does this mean? Can I use this fact to solve the Schroedinger equation using the split operator technique?
And what about the "particle-method" technique? Do you know it? It can be used for a magnetic field?

Last edited by a moderator: May 5, 2017