Projection Operator

$\begin{displaymath} \tilde p \equiv \vert\phi_i(x)\rangle \langle \phi_i(t)\vert \end{displaymath}$

$\begin{displaymath} \tilde p \sum_j c_j\vert\phi_j(t)\rangle = c_i\vert\phi_i(x)\rangle \end{displaymath}$

$\begin{displaymath} \sum_i \vert\phi_i(x)\rangle \langle \phi_i(x)\vert = 1. \end{displaymath}$

See also Bra, Ket