probset12

# probset12 - Physics 5524 Statistical Mechanics Problem Set...

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Physics 5524 Statistical Mechanics Problem Set 12 Due: Wednesday, Apr. 22 11.3 Cont’d. In Problem 11.3 you (hopefully) found that the one-particle density of states for a 2D nonrelativistic gas of spin-1/2 fermions conﬁned to an area A is given by, a ( E ) = A m π ¯ h 2 , E > 0 , ( a ( E ) = 0 for E < 0). (d) Obtain the speciﬁc heat at constant area of this gas in both the low temperature T ± T F and high temperature T >> T F limits. 12.1 Consider a noninteracting gas of ultrarelativistic spin-1/2 fermions with dispersion relation E ( ~ k ) = ¯ hc | ~ k | . The gas consists of N particles in a three-dimensional volume V and so has number density n = N/V . (a) Obtain the one-particle density of states a ( E ) for these fermions. (b) Obtain an expression for the Fermi energy E F of this gas as a function of the density n . (c) Show that at T = 0 the total energy of this gas is E = 3 4 N E F . (d) Use the fact that for an ultrarelativistic gas

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## This note was uploaded on 12/14/2011 for the course PHY 5524 taught by Professor Bonesteel during the Spring '09 term at FSU.

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probset12 - Physics 5524 Statistical Mechanics Problem Set...

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