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Application of WKB method to a magnetization problem

  • Thread starter jannyhuggy
  • Start date
  • #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.

Homework Statement



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.


Homework 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

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:

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