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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 ...
