Introduction to Quantum Mechanics · Problem 4.75

Quantum Mechanics in Three Dimensions — David J. Griffiths

Physics — Quantum Mechanics · aharonov_bohm_time_dependent

Problem

Consider the system of Example 4.6, now with a time-dependent flux

\Phi(t)

through the solenoid. Show that

\Psi(t) = \frac{1}{\sqrt{2\pi}}\,e^{in\phi}\,e^{-if(t)}

with

f(t) = \frac{1}{\hbar}\int_0^t \frac{\hbar^2}{2mb^2}\left(n - \frac{q\,\Phi(t')}{2\pi\hbar}\right)^2 dt'

is a solution to the time-dependent Schrödinger equation.