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classical_microcanonical_phase_volume [2013/11/02 03:28] nikolaj |
classical_microcanonical_phase_volume [2014/03/21 11:11] 127.0.0.1 external edit |
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| ===== Classical microcanonical phase volume === | ===== Classical microcanonical phase volume === | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $ \langle \mathcal M, \mathcal H,\pi,\pi_0,{\hat\rho},{\hat\rho}_0\rangle$ ... classical microcanonical ensemble | | + | | @#55CCEE: context | @#55CCEE: $ \langle \mathcal M, \mathcal H,\pi,\pi_0,{\hat\rho},{\hat\rho}_0\rangle$ ... classical microcanonical ensemble | |
| - | | @#88DDEE: $ \mathrm{dim}(\mathcal M) = 3N $ | | + | | @#55CCEE: context | @#55CCEE: $ \mathrm{dim}(\mathcal M) = 3N $ | |
| - | | @#88DDEE: $ \hbar$ ... Reduced Planck's constant | | + | | @#55CCEE: context | @#55CCEE: $ \hbar$ ... Reduced Planck's constant | |
| - | | @#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 $ | | + | | @#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 $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| === Alternative definitions === | === Alternative definitions === | ||
| - | $\Gamma(E):=\frac{1}{h^{3N}N!}\int_{\Gamma_{\mathcal M}}\ \hat\rho(E;{\bf q},{\bf p}) \ \mathrm d\Gamma $ | + | $\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]]. | And here we see that this is the analog of [[Classical canonical partition function]] for the [[Classical canonical ensemble]]. | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| [[Classical microcanonical ensemble]] | [[Classical microcanonical ensemble]] | ||
