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observable [2014/03/21 11:11] 127.0.0.1 external edit |
observable [2016/01/18 22:08] nikolaj |
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| ==== Set ==== | ==== Set ==== | ||
| | @#55CCEE: context | @#55CCEE: $V$...Hilbert space | | | @#55CCEE: context | @#55CCEE: $V$...Hilbert space | | ||
| - | |||
| | @#FFBB00: definiendum | @#FFBB00: $\mathrm{Observable}(V)\equiv\mathrm{SelfAdjoint}(V)\cap\mathrm{End}(V)$ | | | @#FFBB00: definiendum | @#FFBB00: $\mathrm{Observable}(V)\equiv\mathrm{SelfAdjoint}(V)\cap\mathrm{End}(V)$ | | ||
| + | ----- | ||
| + | === Discussion === | ||
| Observables are the linear self-adjoint operators. | Observables are the linear self-adjoint operators. | ||
| - | ==== Discussion ==== | + | {{ matura_im_mai.jpg?X400}} |
| * $\langle\psi|A\ \phi\rangle\in \mathbb C$ is called //transition amplitude//. | * $\langle\psi|A\ \phi\rangle\in \mathbb C$ is called //transition amplitude//. | ||
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| * $\frac{\langle \psi | A\ \psi \rangle}{\Vert\psi\Vert^2}\in \mathbb R$ is called [[Hilbert space mean value|mean value]]. | * $\frac{\langle \psi | A\ \psi \rangle}{\Vert\psi\Vert^2}\in \mathbb R$ is called [[Hilbert space mean value|mean value]]. | ||
| + | |||
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Self-adjoint_operator|Self-adjoint operator]], [[http://en.wikipedia.org/wiki/Observable|Observable]] | Wikipedia: [[http://en.wikipedia.org/wiki/Self-adjoint_operator|Self-adjoint operator]], [[http://en.wikipedia.org/wiki/Observable|Observable]] | ||
| - | ==== Parents ==== | + | |
| + | ----- | ||
| === Subset of === | === Subset of === | ||
| [[Self-adjoint operator]], [[Vector space endomorphism]] | [[Self-adjoint operator]], [[Vector space endomorphism]] | ||
