# Application of WKB method to a magnetization problem

1. Jul 8, 2012

### jannyhuggy

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
$\dot{M_x}$=2K1MzMy+HzMy-HyMz,

$\dot{M_y}$=-2(K1+K2)MzMx+HxMz-HzMx,

$\dot{M_z}$=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