1. Sommerfeld Expansion in 2D a. Show that every term in the Sommerfeld expansion for density n vanishes except for the T =0 term. Also show that this procedure (erroneously) predicts the exact relationship μ =E F . b. By performing the exact integration analytically, derive the following result: μ +k B T*ln(1+exp(-μ /k B T))=E F c. Using a suitable expansion of the natural log, show that the correction from μ =E F is negligible. d. The conclusion in (a) included all orders of the expansion – so why is there a discrepancy with the exact solution? 2. Free electron gas with an anisotropic dispersion a. Suppose one has a free electron gas in 3D where the dispersion relation is given by
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 12/29/2011 for the course PHYSICS 731 taught by Professor Appelbaum during the Fall '11 term at Maryland.