Problem Set 4 Hint 2

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

Z(Y) = ( L
∏
i=1 +∞
∫
-∞ dw_i) e^-H[w_i]/k_BT δ( L
∑
j=1 w_j - Y)

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

δ(x) = +∞
∫
-∞ dk
2π e^ikx

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