# Are Quantum Physics and statistical theory always the same as semiclassical approximations?

Quantum Mechanics and Statistical physics is a bit hard , could we then study only the WKB approximation ?

In the form:

replace $\sum_{n=0}^{\infty}exp(- \beta E_{n})=Z(\beta)\sim\iint dxdpexp(-p^{2}\beta +\beta V(x))$

and for the Eigenvalue staircase $\sum_{n} \delta (E-E_{n})\sim \iint dxdp \delta (E-p^{2}-V(x))$

so it is easier to evaluate quantities :)

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May I suggest, adding the "soft-question" tag. –  Argus Jun 8 '12 at 21:58
For what purpose? The first you said is classical stat-mech, the second is a uniform density on the energy hypersurface, and it's not the most accurate semi-classical approximation, it has no leading $\hbar$ corrections. –  Ron Maimon Jun 9 '12 at 2:08