Principles of Quantum Mechanics · Problem 18.16

Time-Dependent Perturbation Theory — R. Shankar

Physics — Quantum Mechanics · adiabatic-approximation

Problem

Show that the Berry phase

\gamma_n(t) = i\int_0^t \langle n(t')|\dot{n}(t')\rangle\, dt'

is real. [Hint: Differentiate the normalization condition

\langle n(t)|n(t)\rangle = 1

with respect to

t