|Jul8-12, 04:52 AM||#1|
Application of WKB method to a magnetization problem
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
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?
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