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 classical_ensemble_expectation_value [2013/09/12 21:30]nikolaj classical_ensemble_expectation_value [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2013/09/12 21:30 nikolaj 2013/09/12 21:30 nikolaj 2013/09/12 21:28 nikolaj created Next revision Previous revision 2013/09/12 21:30 nikolaj 2013/09/12 21:30 nikolaj 2013/09/12 21:28 nikolaj created Line 1: Line 1: ===== Classical ensemble expectation value === ===== Classical ensemble expectation value === - ==== Definition ​==== + ==== Set ==== - | @#88DDEE: $\langle \mathcal M, H,​\pi,​\pi_0,​{\hat\rho},​{\hat\rho}_0\rangle$ ... classical statistical ensemble | + | @#55CCEE: context ​    | @#55CCEE: $\langle \mathcal M, H,​\pi,​\pi_0,​{\hat\rho},​{\hat\rho}_0\rangle$ ... classical statistical ensemble | - | @#FFBB00: $\langle \cdot \rangle: (\Gamma_{\mathcal M}\to \mathbb R)\to \mathbb R$ | + | @#FFBB00: definiendum ​| @#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: definiendum ​| @#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 ​=== + === Context ​=== [[Classical probability density function]] [[Classical probability density function]]