[[Functional analysis MOC]]
# Dirac orthonormality

A set of kets $\ket{f_{p}}$ where $p \in \mathbb{R}$ is said to be **Dirac orthonormal**[^2018] iff #m/def/anal/fun 
$$
\begin{align*}
\braket{ f_{p'} | f_{p'} } = \delta(p-p) 
\end{align*}
$$
where $\delta$ is the [[Dirac delta]],
and in addition complete iff
$$
\begin{align*}
\int _{D} \ket{f_{z}} \bra{f_{z}}  \, dz = \mathbf{I}
\end{align*}
$$

[^2018]: 2018\. [[Sources/@griffithsIntroductionQuantumMechanics2018|Introduction to quantum mechanics]], §3.3.2, p. 100


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