MIT OpenCourseWare http ocw mit edu 8 512 Theory of Solids II Spring 2009 For information about citing these materials or our Terms of Use visit http ocw mit edu terms 1 8 512 Theory of Solids II Problem Set 6 Due March 31 2008 1 The response function K de ned by J K A can be decomposed into the transverse and longitudinal parts q q q q K q 2 K q 2 Kk q q q a Starting from the linear response expression calculate K q 0 for a free Fermi gas It may be useful to choose q qz and compute Kxx b Using the results from a show that the Landau diamagnetic susceptibility in cluding spin degeneracy is given by D e2 kF 12 2 mc2 Check that this is 1 3 of the Pauli spin susceptibility For an alternative deriva tion using Landau levels please study the discussion in Landau and Lifshitz s Statistical Physics Vol 1 p 173
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