= Bra-ket notation
{title2=$|\psi\rangle,\quad\langle\psi|$}
= Dirac notation
{c}
{synonym}
A ket $|\psi\rangle$ denotes a <vector> representing a <quantum state>, and its bra $\langle\psi|$ is the linear functional taking $|\phi\rangle$ to $\langle\psi|\phi\rangle$. The map from a ket to its bra is conjugate-linear. In the physics convention, $\langle\psi|\phi\rangle$ is conjugate-linear in $\psi$ and linear in $\phi$. The <adjoint operator> is characterized by $\langle\psi|A\phi\rangle=\langle A^*\psi|\phi\rangle$. Products such as $|\psi\rangle\langle\phi|$ are rank-one operators, while $\langle\phi|\psi\rangle$ is a scalar <inner product>.
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