===== Classical microcanonical phase volume ===
==== Set ====
| @#55CCEE: context     | @#55CCEE: $ \langle \mathcal M, \mathcal H,\pi,\pi_0,{\hat\rho},{\hat\rho}_0\rangle$ ... classical microcanonical ensemble |
| @#55CCEE: context     | @#55CCEE: $ \mathrm{dim}(\mathcal M) = 3N $ |
| @#55CCEE: context     | @#55CCEE: $ \hbar$ ... Reduced Planck's constant | 
| @#FFBB00: definiendum | @#FFBB00: $\Gamma(E):=\frac{1}{h^{3N} N!}\int_{\{\langle{\bf q},{\bf p}\rangle\in \Gamma_{\mathcal M}\ |\ E\le H({\bf q},{\bf p})\le E+\Delta\}} \mathrm d\Gamma $ |

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=== Discussion ===
=== Alternative definitions ===

$\Gamma(E):=\frac{1}{h^{3N}N!}\int_{\Gamma_{\mathcal M}} \hat\rho(E;{\bf q},{\bf p}) \ \mathrm d\Gamma $

And here we see that this is the analog of [[Classical canonical partition function]] for the [[Classical canonical ensemble]].

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=== Context ===
[[Classical microcanonical ensemble]]