Boltzman:

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Physics 418: Statistical Mechanics I
Prof. S. Teitel stte@pas.rochester.edu ----- Spring 2005

Set3 Hint2

Handle the constraint by using a delta-function in the partition function summation,

Z(Y) = ( L
prod
i=1
+infty
int
-infty
dwi) e-H[wi]/kBT delta( L
sum
j=1
wj - Y)

and then use the Fourier transform representation of the delta-function,

delta(x) = +infty
int
-infty
dk
2pi
ei kx

Do the integrals over the wi first, and the integral over k last. Things should factor nicely!


Last update: Wednesday, August 22, 2007 at 1:09:01 PM.