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Spin angular momentum operators

  1. Aug 22, 2007 #1
    I posted this is in the QM section but maybe here would have been better. I don't think it is a hard question for any one who knows QM:

    Last edited: Aug 22, 2007
  2. jcsd
  3. Aug 23, 2007 #2
    Okay, I want to know the answer enough that I will repost the question here:

    The dipolar coupling Hamiltonian expressed in the lab frame (units of Hz) is

    [tex] H ^D_{ij} = - constants/r_{ij}^3 * I_{iz} * I_{jz} * P_2(\cos(\theta))[/tex]

    where r_ij is the internuclear distance between spins, ci and cj are the gyromagnetic ratios of spins i and j, and I_kz are spin angular momentum operators. The angular portion of the
    dipolar Hamiltonian is described using the second rank Legendre function, P_2(cos h(t)),
    which is a function of the angle h subtending the magnetic field and the ijth internuclear

    Somehow they go from that equation to the following one:

    [tex]D^{resultant}_{ij} = constants * < P_2(cos(\theta(t))/r_{ij}^3)> [/tex]
    Last edited: Aug 23, 2007
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