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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.

I have to go from classical to quantum Hamiltonian via WKB method (and both to solve Schroedinger equation)

It looks like E=-K

I've got the system of equations of motion for classical case

[itex]\dot{M_x}[/itex]=2K

[itex]\dot{M_y}[/itex]=-2(K

[itex]\dot{M_z}[/itex]=2K

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?

## Homework Statement

I have to go from classical to quantum Hamiltonian via WKB method (and both to solve Schroedinger equation)

It looks like E=-K

_{1}M_{z}^{2}+K_{2}M_{x}^{2}-(H,M). H =(H_{x},H_{y},H_{z}) - external magnetic field, constant in time, M^{2}=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]=2K

_{1}M_{z}M_{y}+H_{z}M_{y}-H_{y}M_{z},[itex]\dot{M_y}[/itex]=-2(K

_{1}+K_{2})M_{z}M_{x}+H_{x}M_{z}-H_{z}M_{x},[itex]\dot{M_z}[/itex]=2K

_{2}M_{x}M_{y}+H_{y}M_{x}-H_{x}M_{y}## 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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