Principles of Quantum Mechanics · Problem 7.4.6

The Path Integral Formulation of Quantum Theory — R. Shankar

Physics — Quantum Mechanics · ladder-operator-time-evolution

Problem

Show that

\langle a(t)\rangle = e^{-i\omega t}\langle a(0)\rangle

and that

\langle a^\dagger(t)\rangle = e^{i\omega t}\langle a^\dagger(0)\rangle