## Beyond semiclassical approach

let be $$E_n$$ the set of values of a given Hamiltonian H=H(p,q) , then if we wished to calculate the following sum

$$\sum_{n >0} exp (-uE_n )$$ for real valued and positive 'u' then the semiclassical approximation gives

$$\sum_{n >0} exp (-uE_n ) = \iint _{P}dqdp exp(-uH(q,p))$$

is this the best approximation we can use ?,
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