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classical_ensemble_expectation_value [2013/09/12 21:28] nikolaj created |
classical_ensemble_expectation_value [2013/09/12 21:30] nikolaj |
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| | @#88DDEE: $ \langle \mathcal M, H,\pi,\pi_0,{\hat\rho},{\hat\rho}_0\rangle$ ... classical statistical ensemble | | | @#88DDEE: $ \langle \mathcal M, H,\pi,\pi_0,{\hat\rho},{\hat\rho}_0\rangle$ ... classical statistical ensemble | | ||
| - | | @#FFBB00: $\langle \cdot \rangle:\Gamma_{\mathcal M}\to \mathbb R\to \mathbb R$ | | + | | @#FFBB00: $\langle \cdot \rangle: (\Gamma_{\mathcal M}\to \mathbb R)\to \mathbb R$ | |
| | @#FFBB00: $\langle F\rangle:=\int_{\Gamma_{\mathcal M}}\ F\cdot\rho\ \mathrm d\Gamma$ | | | @#FFBB00: $\langle F\rangle:=\int_{\Gamma_{\mathcal M}}\ F\cdot\rho\ \mathrm d\Gamma$ | | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
| - | The function $\rho$ is just the normalized version of ${\hat\rho}$. | + | In the definition we must use $\rho$, i.e. the noramlized ${\hat\rho}$. |
| ==== Parents ==== | ==== Parents ==== | ||
| === Requirements === | === Requirements === | ||
| [[Classical probability density function]] | [[Classical probability density function]] | ||
