Principles of Quantum Mechanics · Problem 1.9.2

Mathematical Introduction — R. Shankar

Physics — Quantum Mechanics · functions-of-operators-unitary

Problem

H

is a Hermitian operator, show that

U = e^{iH}

is unitary. (Notice the analogy with

c

numbers: if

\theta

is real,

u = e^{i\theta}

is a number of unit modulus.)