# Quantum mechanics

1. Nov 6, 2007

### noospace

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

Determine the energy levels, their degeneracy and wave functions (in ket notation) of a particle with spin quantum number s =1 if the Hamiltonian is $AS_x^2 + AS_y^2 + B S_z^2$ where A and B are constants.

3. The attempt at a solution'

I've spent ages thinking about this but I keep finding that the Hamiltonian is $(\hbar^2/4)(2A + B)I$ where I is the identity matrix. This is very strange since it implies that there are an infinite number of eigenstates with identically the same eigenvalue!

2. Nov 6, 2007

### malawi_glenn

What matrices did you use for the S_x etc? Not the pauli matrices right? They are only valid for spin 1/2 partilces.

3. Nov 6, 2007

### clem

$AS_x^2 + AS_y^2 + B S_z^2=AS^2+(B-A)S_z^2.$
You know S^2. There are three values of S_z, and two of S_z^2.
You don't need to know any matrices.

4. Nov 6, 2007

### noospace

Hi clem and malawi_glenn,

Thanks heaps for pointing out my mistake.