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View Full Version : Sum of Eigenvalues...(strange partition function)


lokofer
Sep21-06, 11:27 AM
Let's suppose we have a system of energies so E(-n)=-E(n) then we define u=1/T (temperature) the sum:

Z= \sum_{n=-\infty}^{\infty}e^{iuE(n)}

Then my question is if the equalities are satisfied:

Z=Tr(e^{iuH})\sim \iint_{R^2}dxdpe^{iup^2 +iuV(x)} with

H\Phi =E(n)\Phi=(p^2 +V(x))\Phi and Z=Z^{*}

The first equality is "exact" the second is just "asymptotic" or approximate...:redface: :redface: