445lec30 - PHYS 445 Lecture 30 - Low temperature Fermi gas...

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PHYS 445 Lecture 30 - Low temperature Fermi gas 30 - 1 © 2001 by David Boal, Simon Fraser University. All rights reserved; further resale or copying is strictly prohibited. Lecture 30 - Low temperature Fermi gas What's Important: heat capacity for ideal Fermi gas Text : Reif Heat capacity for ideal Fermi gas This lecture contains a somewhat lengthy mathematical examination of non-interacting Fermi gases at low temperatures. First, the mean energy E of the gas is determined, which permits the calculation of the heat capacity C v via C v = E T (30.1) Mean energy As shown in previous lectures, a gas of fermions without interactions obeys the number distribution n i = 1 e ß ( i - ) + 1 , (30.2) where μ is alternatively the Fermi energy F . Converting this to a continuum distribution gives the mean number of electrons in the momentum range p to p + d p as n ( p ) d 3 p = 2 V h 3 d 3 p e ß ( i - ) + 1 where the factor of two comes from the spin-1/2 nature of the electrons. For the problem at hand, it is more useful to know the distribution of electron energies, rather
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This note was uploaded on 09/07/2009 for the course PHYS 445 taught by Professor Davidboal during the Spring '08 term at Simon Fraser.

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445lec30 - PHYS 445 Lecture 30 - Low temperature Fermi gas...

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