In

Quantum Mechanics, an operator is called unitary if its

hermitian adjoint is equal to its

inverse, ie. U

^{+}U = UU

^{+} = 1.

Unitary operators can be used to describe

symmetries of the space of quantum states; due to their property that they preserve the hermitian

inner product: that is to say, if under some transfromation |A

> goes to U|A

> and |B

> goes to U|B

>, then

<B| goes to

<B|U

^{+}, and then