===== Observable =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $V$...Hilbert space |
| @#FFBB00: definiendum | @#FFBB00: $\mathrm{Observable}(V)\equiv\mathrm{SelfAdjoint}(V)\cap\mathrm{End}(V)$ |

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=== Discussion ===
Observables are the linear self-adjoint operators.

{{ matura_im_mai.jpg?X400}}

  * $\langle\psi|A\ \phi\rangle\in \mathbb C$ is called //transition amplitude//.

  * $\frac{|\langle\psi|A\ \phi\rangle|^2}{\Vert\psi\Vert^2\Vert\psi\Vert^2}\ge 0$ is called //transition probability//.

  * $\langle \psi | A\ \psi \rangle\in \mathbb R$ is called [[Hilbert space expectation value|expectation value]].

  * $\frac{\langle \psi | A\ \psi \rangle}{\Vert\psi\Vert^2}\in \mathbb R$ is called [[Hilbert space mean value|mean value]].

=== Reference ===
Wikipedia: [[http://en.wikipedia.org/wiki/Self-adjoint_operator|Self-adjoint operator]], [[http://en.wikipedia.org/wiki/Observable|Observable]]

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=== Subset of ===
[[Self-adjoint operator]], [[Vector space endomorphism]]