(adsbygoogle = window.adsbygoogle || []).push({}); Does this hold in general ?? (as an approximation only)

for every real or pure complex number 'a' can we use as an approximation:

[tex] \sum _{n} exp(-aE_{n}) \sim \int_{-\infty}^{\infty} dx \int_{-\infty}^{\infty} dp exp(-ap^{2}-aV(x)) [/tex]

So for every x V(x) > 0 in case of real and positive a ... then i would like to know if this approximation could be useful to describe the 'Semi-classical behaviour' of the sum over energies (trace) replaced by an integral.

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# Does this hold in general ? (as an approximation only)

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