Unitary Operators

Unitary operators preserve a scalar product.

\begin{displaymath}\bgroup\color{black}\langle\phi\vert\psi\rangle=\langle U\phi\vert U\psi\rangle=\langle\phi\vert U^\dagger U\psi\rangle \egroup\end{displaymath}

This means that

\begin{displaymath}\bgroup\color{black}U^\dagger U=1 .\egroup\end{displaymath}

Unitary operators will be important for the matrix representation of operators. The will allow us to change from one orthonormal basis to another.



Jim Branson 2013-04-22