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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 ====
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 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]]
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