A Modern Approach to Quantum Mechanics · Problem 4.2

A System of Two Spin-1/2 Particles — John S. Townsend

Physics — Quantum Mechanics · time-dependent-hamiltonian-evolution-operator

Problem

Show that if the Hamiltonian depends on time and

[\hat{H}(t_1), \hat{H}(t_2)] = 0

, the time-development operator is given by

\hat{U}(t) = \exp\left[-\frac{i}{\hbar}\int_0^t dt'\, \hat{H}(t')\right]