ps2 - Physics 880.06 Problem Set 2 Due Monday April 18 by...

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Unformatted text preview: Physics 880.06: Problem Set 2 Due Monday, April 18 by 11:59 P. M. 1. 20 pts. (a). Consider a free electron gas of density n electrons per unit volume (in three dimensions). Calculate the electronic density of states N(E) (in states per unit energy per unit volume). Show, in particular that N ( E ) = A √ E , and calculate the constant A in terms of fundamental constants (i. e. ¯ h , electron mass, and electronic charge, if they enter) and the density n. (b). Calculate the Fermi energy E F in terms of n. (c). Hence, find N ( E F ). (d). Find the actual numerical values of these quantities for the metal aluminum, assuming that there are three valence electrons per atom. (e). Repeat (a) - (c) for a two-dimensional electron gas, except that n is understood now as the electron density per unit area. 2. (10 pts.) We showed in class that the relative wave function of a Cooper pair is proportional to summationdisplay k>k F cos k · r 2 ξ k + 2 E F − E , (1) where (as stated in class) ξ k...
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ps2 - Physics 880.06 Problem Set 2 Due Monday April 18 by...

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