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445lec23

# 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(- α N ) to form Z = Σ N' exp(- α N' ) Z ( N' ) where N = n 1 + n 2 + n 3 ... and ln Z = - α 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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445lec23 - PHYS 445 Lecture 23 Fermions 23 1 © 2001 by...

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