2
votes
0answers
106 views

Trace of the number operator in second quantization

I would like to find the helmholtz free energy of a system $F=-T ln(Tr[e^{\frac{-H}{T}}])$ namely a bcs superconductor (using Annett's notation) $H=\sum E_k (b_{k\uparrow}^\dagger ...
3
votes
2answers
286 views

Density of states via a Laplace transform

Is this formula correct? $$ \frac{-1}{\pi}Im\int_{0}^{\infty}\!dt~\exp(Et)\Theta (t)\exp(i \epsilon t) ~=~ \sum _{n}\delta (E-E_{n}), $$ $$ \Theta (t)~=~ \sum_{n}\exp(-tE_{n}) ,$$ and I have used ...