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

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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 $|\phi\!\!>$.

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    $\begingroup$ Usually \langle and \rangle are preferred over < and < as delimiters $\ddot\smile$ $\endgroup$ Aug 30, 2017 at 23:31
  • $\begingroup$ Yes, I didn't know about those because they are not in the original LaTeX book I have. But this at least gave me the chance to use \! a few times! $\endgroup$ Sep 10, 2017 at 16:15
  • $\begingroup$ Have you seen this MathJax tutorial before? I find it very helpful. $\endgroup$ Sep 10, 2017 at 17:36

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