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hilbert_space_expectation_value [2013/09/06 22:04] 127.0.0.1 external edit |
hilbert_space_expectation_value [2014/03/21 11:11] (current) |
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| ===== 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 ==== | ||
| === Theorems === | === Theorems === | ||
| - | $A\ \psi=\lambda\ \psi \implies \langle A \rangle_{\psi}=\lambda\ \land\ \Delta_\psi A=0$ | + | ^ $A\ \psi=\lambda\ \psi \implies (\langle A \rangle_{\psi}=\lambda)\,\land\,(\Delta_\psi A=0)$ ^ |
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| [[Hilbert space]], [[Observable]] | [[Hilbert space]], [[Observable]] | ||
| + | === Related === | ||
| + | [[Hilbert space mean value]] | ||
