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 classical_confined_phase_volume [2013/10/21 23:00]nikolaj classical_confined_phase_volume [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2013/10/27 16:50 nikolaj 2013/10/21 23:00 nikolaj 2013/10/13 14:56 nikolaj 2013/10/13 03:55 nikolaj 2013/09/11 22:53 nikolaj created Next revision Previous revision 2013/10/27 16:50 nikolaj 2013/10/21 23:00 nikolaj 2013/10/13 14:56 nikolaj 2013/10/13 03:55 nikolaj 2013/09/11 22:53 nikolaj created Line 1: Line 1: ===== Classical confined phase volume === ===== Classical confined 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: $\varphi(E):​=\frac{1}{h^{3N} N!}\int_{\{\langle{\bf q},{\bf p}\rangle\in \Gamma_{\mathcal M}\ |\ H({\bf q},{\bf p})\le E\}} \mathrm d\Gamma$ | + | @#FFBB00: definiendum ​| @#FFBB00: $\varphi(E):​=\frac{1}{h^{3N} N!}\int_{\{\langle{\bf q},{\bf p}\rangle\in \Gamma_{\mathcal M}\ |\ H({\bf q},{\bf p})\le E\}} \mathrm d\Gamma$ | ==== Discussion ==== ==== Discussion ==== ==== Parents ==== ==== Parents ==== - === Requirements ​=== + === Context ​=== - [[Classical microcanonical ensemble]], [[Planck'​s constant]] + [[Classical microcanonical ensemble]] 