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 hilbert_space_expectation_value [2013/09/11 17:05]nikolaj hilbert_space_expectation_value [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2013/09/11 17:07 nikolaj 2013/09/11 17:05 nikolaj 2013/09/06 22:04 external edit2013/08/31 22:37 nikolaj 2013/08/31 22:36 nikolaj 2013/08/31 21:41 nikolaj 2013/08/31 21:33 nikolaj 2013/08/31 21:33 nikolaj created Next revision Previous revision 2013/09/11 17:07 nikolaj 2013/09/11 17:05 nikolaj 2013/09/06 22:04 external edit2013/08/31 22:37 nikolaj 2013/08/31 22:36 nikolaj 2013/08/31 21:41 nikolaj 2013/08/31 21:33 nikolaj 2013/08/31 21:33 nikolaj created Line 1: Line 1: ===== Hilbert space expectation value ===== ===== Hilbert space expectation value ===== - ==== Definition ​==== + ==== Set ==== - | @#88DDEE: $V$...Hilbert space | + | @#55CCEE: context ​    | @#55CCEE: $V$...Hilbert space | - | @#FFBB00: $\langle\cdot\rangle_{-}:​\mathrm{Observable}(V)\times V\to\mathbb R$ | + | @#FFBB00: definiendum ​| @#FFBB00: $\langle\cdot\rangle_{-}:​\mathrm{Observable}(V)\times V\to\mathbb R$ | - | @#FFBB00: $\langle A \rangle_{\psi}:​=\langle \psi | A\ \psi \rangle$ | + | @#FFBB00: definiendum ​| @#FFBB00: $\langle A \rangle_{\psi}:​=\langle \psi | A\ \psi \rangle$ | ==== Discussion ==== ==== Discussion ==== Line 10: Line 10: ^ $A\ \psi=\lambda\ \psi \implies (\langle A \rangle_{\psi}=\lambda)\,​\land\,​(\Delta_\psi A=0)$ ^ ^ $A\ \psi=\lambda\ \psi \implies (\langle A \rangle_{\psi}=\lambda)\,​\land\,​(\Delta_\psi A=0)$ ^ ==== Parents ==== ==== Parents ==== - === Requirements ​=== + === Context ​=== [[Hilbert space]], [[Observable]] [[Hilbert space]], [[Observable]] + === Related === + [[Hilbert space mean value]]