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Numerical solution of SE

  1. Jun 20, 2011 #1
    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:
    [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?
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
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