1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding magnetic susceptibility of a quantum gas

  1. Nov 22, 2007 #1
    1. The problem statement, all variables and given/known data
    H=H[tex]_{0}[/tex] -g[tex]\mu[/tex]SB
    H[tex]_{0}[/tex] = hamiltonian in absence of field
    S=Spin operator in the direction of the fied (say along z-axis)

    show that
    1) M=1/[tex]\beta[/tex] (dLn Z/ dB)

    2) [tex]\chi[/tex] = [tex]\beta[/tex](g [tex]\mu[/tex])[tex]^{2}[/tex] <(S-<S>)[tex]^{}2[/tex]>

    Dont know why it shows[tex]\mu[/tex] in superscript. It isnt meant to be!
    That is the chemical potential.

    2. Relevant equations
    Canonical partition function for a grand ensemble is

    3. The attempt at a solution

    I know that M=g[tex]\mu[/tex]<S>

    I dont know how to go about differentiating Ln Z w.r.t B

    For the second part, I used the given result and differentiated it w.r.t B again.
    I get [tex]\beta[/tex]times some junk! I cant get to the required result. I have a feeling its very poor math on my part. Any leads from here on would be well received.
  2. jcsd
  3. Nov 22, 2007 #2
    got it

    Cant stop laighing at myself.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Finding magnetic susceptibility of a quantum gas