Lecture13

1 2 principle of microscopic reversibility n1n2 n3

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Unformatted text preview: quantum par?cles. k 7 Boson staHsHcs •  We’ve already seen that bosons display some tendency to want to be in the same state (recall our calculaHon of the average separaHon) •  Einstein: TransiHon rate into parHcular boson state populaHon n is enhanced by a factor of n+1. R(1 + 2 ! 3 + 4 ) = Cn1n2 (n3 + 1)(n4 + 1) R(1 + 2 ! 3 + 4 ) = R( 3 + 4 ! 1 + 2 ) (principle of microscopic reversibility) n1n2 (n3 + 1)(n4 + 1) = n3n4 (n1 + 1)(n2 + 1) ! n1 $ ! n2 $ ! n3 $ ! n4 $ ln # & + ln # & = ln # & + ln # & n1 + 1 % n2 + 1 % n3 + 1 % n4 + 1 % " " " " E1 + E2 = E3 + E4 !n$ ln # & = ' (µ ( E ) " n +1 % 1 n( E ) = exp ( ! ( E " µ ) ) " 1 8 Bose ­Einstein DistribuHon 1 Forgot to include spin. For every state of spin s n( E ) = exp ( ! ( E " µ ) ) " 1 there are 2s+1 states n( E ) = (2 s + 1) exp ( ! ( E " µ ) ) " 1 What are β and μ? For large T, we must regain the Boltzmann distribuHon to reproduce classical physics n( E ) ! exp(" # E ) ! n( E ) = N For normalizaHon: β = 1/kT • Since N > 0 so exp() > 1. •...
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This document was uploaded on 02/04/2014.

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