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Application of WKB method to a magnetization problem

  1. Jul 8, 2012 #1
    It is not from my howework(due I'm not in the undergrad now), but it seems to be a very easy question I have to know answer to, but I fail to do so.

    1. The problem statement, all variables and given/known data

    I have to go from classical to quantum Hamiltonian via WKB method (and both to solve Schroedinger equation)
    It looks like E=-K1Mz2+K2Mx2-(H,M). H =(Hx,Hy,Hz) - external magnetic field, constant in time, M2=const. Here M is the magnetization vector.


    2. Relevant equations
    I've got the system of equations of motion for classical case
    [itex]\dot{M_x}[/itex]=2K1MzMy+HzMy-HyMz,

    [itex]\dot{M_y}[/itex]=-2(K1+K2)MzMx+HxMz-HzMx,

    [itex]\dot{M_z}[/itex]=2K2MxMy+HyMx-HxMy

    3. The attempt at a solution

    Then I need to use WKB method, and I have 2 variables. When I write down the Schroedinger equation I either need to separate variables (and then solve using WKB like hydrogen atom) or to use multiple-variables WKB method if they cannot be separated.

    Both in xyz and spherical (if I didn't do any mistake) I cannot separate variables in Schroedinger equation.
    Any ideas how to apply WKB here (or ideas of I did mistakes)?

    So, the question is
    - to help me check whether in any coordinate system variables can be separated, if yes - in which one?
    - if they cannot - how to apply 2-variable WKB method here?
     
    Last edited: Jul 8, 2012
  2. jcsd
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