Observable

Set

 context $V$…Hilbert space definiendum $\mathrm{Observable}(V)\equiv\mathrm{SelfAdjoint}(V)\cap\mathrm{End}(V)$

Discussion

Observables are the linear self-adjoint operators.

• $\langle\psi|A\ \phi\rangle\in \mathbb C$ 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.
• $\frac{\langle \psi | A\ \psi \rangle}{\Vert\psi\Vert^2}\in \mathbb R$ is called mean value.