Problem Set 2 Hint 3

OK, here it is.

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

Z(Y) = ( L
prod
i=1 + infty
int
- infty dw_i) e^-H[w_i]/k_BT delta ( L
sum
j=1 w_j - Y)

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

delta (x) = + infty
int
- infty dk
2 e^{i kx}

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

Last update: Wednesday, August 22, 2007 at 3:20:29 PM.