# What is the intuitive meaning of outer product in Hilbert space

What is the intuitive meaning of outer product of $|\psi\rangle\langle\psi |$ in Hilbert space?

It is the projection operator of some state $|\phi\!\!>$ onto $|\psi\!\!>$.
For example, if $|\psi\!\!>$ is a state of some definite momentum $p$, and $|\phi\!\!>$ some state of uncertain momentum and position, then $|\psi\!\!><\!\!\psi| \phi\!\!>$ selects the momentum = $p$ component of $|\phi\!\!>$.
• Usually \langle and \rangle are preferred over < and < as delimiters $\ddot\smile$ Aug 30, 2017 at 23:31