QM 1st order perturbation theory

  • #1

Homework Statement


Material contains [tex]10^{19}[/tex]/[tex]cm^{3}[/tex] [tex]Cr^{3\frac{1}{2}}[/tex].
in the state [tex]\Psi[/tex](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


Homework Equations



Probably Angular momentum wavefunctions and equations, Spin Matrices


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:

[itex]
\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
[/itex]
For this DC field, I think we have to apply first order perturbation theory in the following:

Perturbation Hamiltonian : hbar*g*([tex]\frac{e}{2m}[/tex])L.B

Any ideas if this is right or wrong?

Thanks
 

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