A Modern Approach to Quantum Mechanics · Problem 2.23

Angular Momentum — John S. Townsend

Physics — Quantum Mechanics · unitary-operators-orthonormal-basis-eigenvalues

Problem

(a) Show that if the states

|a_n\rangle

form an orthonormal basis, so do the states

\hat{U}|a_n\rangle

, provided

\hat{U}

is unitary. (b) Show that the eigenvalues of a unitary operator can be written as

e^{i\theta}