445lec23 - PHYS 445 Lecture 23 - Fermions 23 - 1 2001 by...

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Unformatted text preview: PHYS 445 Lecture 23 - Fermions 23 - 1 2001 by David Boal, Simon Fraser University. All rights reserved; further resale or copying is strictly prohibited. Lecture 23 - Fermions What's Important: Fermi-Dirac statistics comparisons among distributions Fermi energy Text : Reif Fermi-Dirac statistics The Fermi-Dirac distribution can be handled in a similar way to the Bose-Einstein system. Start with the partition function Z = e ! " ( n 1 # 1 + n 2 # 2 + n 3 # 3 + ...) R $ and multiply by exp(- N ) to form Z = N' exp(- N' ) Z ( N' ) where N = n 1 + n 2 + n 3 ... and ln Z = - N + ln Z ( N ) (23.1) Thus Z = e ! " ( n 1 # 1 + n 2 # 2 + n 3 # 3 + ...) ! $ ( n 1 + n 2 + n 3 + ...) n 1 , n 2 , n 3 ... % = e ! ( $ + "# 1 ) n 1 n 1 = 0,1 % & ( ) * + e ! ( $ + "# 2 ) n 2 n 2 = 0,1 % & ( ) * + ... (23.2) Because a given energy state can be occupied by only one particle at the most, each term in brackets has only two contributions, and becomes 1 + e ! ( " + #$ 1 ) Taking the logarithm of Eq.(23.2) then gives a series Taking the logarithm of Eq....
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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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445lec23 - PHYS 445 Lecture 23 - Fermions 23 - 1 2001 by...

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