Hi there!(adsbygoogle = window.adsbygoogle || []).push({});

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:

[tex]H(\vec x, \vec p)=H_1(\vec x)+H_2(\vec p)[/tex]

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:

[tex](p_x+By)^2[/tex]

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?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Numerical solution of SE

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Numerical solution | Date |
---|---|

I Numerical solution of Schrödinger equation | Dec 9, 2016 |

Numerical solution of SE for cylindrical well | Sep 20, 2015 |

Numerical solution of Schrodinger equation | Sep 5, 2015 |

Schrodinger equation numerical solution | Aug 23, 2015 |

Numerically solutions with periodic boundary conditions | Sep 22, 2014 |

**Physics Forums - The Fusion of Science and Community**