- #1

Vitani11

- 275

- 3

## Homework Statement

Show that if H is a hermitian operator, then U = e

^{iH}is unitary.

## Homework Equations

UU

^{†}= I for a unitary matrix

A

^{†}=A for hermitian operator

I = identity matrix

## The Attempt at a Solution

Here is what I have. U = e

^{iH}multiplying both by U

^{†}gives UU

^{†}= e

^{iH}U

^{†}then replacing U

^{†}with U

^{-1}(a property of unitary matrices) I have UU

^{†}= e

^{iH}U

^{-1}and so UU

^{†}= e

^{iH}e

^{-iH}= e

^{i(H-H)}=e

^{0}= 1 = I. I don't think this is right though...