Hilbert space expectation value

Set

context $V$…Hilbert space
definiendum $\langle\cdot\rangle_{-}:\mathrm{Observable}(V)\times V\to\mathbb R$
definiendum $\langle A \rangle_{\psi}:=\langle \psi | A\ \psi \rangle$

Discussion

Theorems

$A\ \psi=\lambda\ \psi \implies (\langle A \rangle_{\psi}=\lambda)\,\land\,(\Delta_\psi A=0)$

Parents

Context

Hilbert space, Observable

Hilbert space mean value