# QM 1st order perturbation theory

1. Apr 17, 2009

### quantumdude10

1. The problem statement, all variables and given/known data
Material contains $$10^{19}$$/$$cm^{3}$$ $$Cr^{3\frac{1}{2}}$$.
in the state $$\Psi$$(l=0, s = 3/2) with fourfold degenerate ground states. When a DC magnetic Field in x-direction is applied to the material, the spin degeneracy is lifted. At near Zero absolute temperature, only ground states are occupied.

The Question:

Determine the Value of the DC magnetic field if the resultant Zeeman level seperations will result in the absorption of a 10GHz signal propagating in the material

2. Relevant equations

Probably Angular momentum wavefunctions and equations, Spin Matrices

3. The attempt at a solution

Given that the Material is at Near Zero absolute temperature, I think the Wavefunctions that we have to worry about are for the following spins:

$\left|\frac{3}{2},\frac{3}{2}\right\rangle, \left|\frac{3}{2},\frac{1}{2}\right\rangle \left|\frac{3}{2},-\frac{1}{2}\right\rangle \left|\frac{3}{2},-\frac{3}{2}\right\rangle$
For this DC field, I think we have to apply first order perturbation theory in the following:

Perturbation Hamiltonian : hbar*g*($$\frac{e}{2m}$$)L.B

Any ideas if this is right or wrong?

Thanks