Introduction to Quantum Mechanics · Problem 6.2

Symmetries and Conservation Laws — David J. Griffiths

Physics — Quantum Mechanics · unitary_operators

Problem

Show that, for a Hermitian operator Q^\hat{Q}, the operator U^=exp⁡[iQ^]\hat{U} = \exp\left[i \hat{Q}\right] is unitary. Hint: First you need to prove that the adjoint is given by U^†=exp⁡[−iQ^]\hat{U}^\dagger = \exp\left[-i \hat{Q}\right]; then prove that U^†U^=1\hat{U}^\dagger \hat{U} = 1. Problem 3.5 may help.

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