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Homework Help: QM 1st order perturbation theory

  1. Apr 17, 2009 #1
    1. The problem statement, all variables and given/known data
    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

    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*([tex]\frac{e}{2m}[/tex])L.B

    Any ideas if this is right or wrong?

  2. jcsd
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