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445lec22 - PHYS 445 Lecture 22 Bosons Lecture 22 Bosons...

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PHYS 445 Lecture 22 - Bosons 22 - 1 © 2001 by David Boal, Simon Fraser University. All rights reserved; further resale or copying is strictly prohibited. Lecture 22 - Bosons What's Important: partition function number distribution condensation Text : Reif Boson partition function We now tackle the general problem of Bose-Einstein statistics. The situation is more difficult than pure photons because the sum over n i is now restricted by the fixed value of the particle number N . It should not surprise us to see a chemical potential appear to enforce the constraint on N . As usual, we start with the generic partition function Z = exp( - ßn 1 1 - ßn 2 2 ...) R (22.1) which is now subject to the constraint Σ i n i = N . (22.2) A mathematical trick is introduced to enforce the constraint. Viewing Z as a function of N , its behaviour is Now, if we multiply the rapidly-increasing function Z ( N ) by a rapidly-decreasing function exp(- N ) we can produce a distribution with a sharp spike at the desired value of N : N Z ( N ) rapidly increasing N' exp(- N' ) N' Z ( N' ) times
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