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Hilbert space expectation value

Definition

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

Discussion

Theorems

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

Parents

Requirements

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