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Band structure and dispersion relations

  1. Aug 26, 2006 #1
    -Let's suppose we have 2 gases ..one is a "Fermi" gas under an Harmonic potential and the other is a "Bose" gas under another Harmonic potential... in both cases (as an approximation) the particles (bosons and electrons are Non-interacting) then we could write the partition functions.

    [tex] \prod _{k=1}^{\infty}(1+be^{\beta \omega (k)})^{-1} [/tex]

    Where "b" is a constant equal to 1 (electrons) or -1 (bosons)..my question is HOw could we calculate the "band structure" for the Fermion gas... ┬┐are the band structure and dispersion relations the "same" concept but one is valid for Bosons and other for Fermions?.. I've read "Ashcroft: Solid State..." where you can find lot's of method to calculate band structure..but what's the best?.., Is there a differential equation or other type of equation satisfied for the [tex] \omega (k) [/tex] in the "Fermionic" case?..thanks.
    Last edited: Aug 26, 2006
  2. jcsd
  3. Sep 4, 2006 #2
    calculate n(e) i.e the density of states. You keep referring to a dispersion relation, and this euphimism of dispersion relation for w(k). you already know what w(k) is if you know the partition function and hence the energy spectrum. i think you are getting confused with terminogy here as you have presented the same question before and it does not make sense.
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