Classical confined phase volume

Set

context $ \langle \mathcal M, \mathcal H,\pi,\pi_0,{\hat\rho},{\hat\rho}_0\rangle$ … classical microcanonical ensemble
context $ \mathrm{dim}(\mathcal M) = 3N $
context $ \hbar$ … Reduced Planck's constant
definiendum $\varphi(E):=\frac{1}{h^{3N} N!}\int_{\{\langle{\bf q},{\bf p}\rangle\in \Gamma_{\mathcal M}\ |\ H({\bf q},{\bf p})\le E\}} \mathrm d\Gamma $

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