Introduction to Quantum Mechanics · Problem 2.38

Time-Independent Schrödinger Equation — David J. Griffiths

Physics — Quantum Mechanics · quantum_revival

Problem

(a) Show that the wave function of a particle in the infinite square well returns to its original form after a quantum revival time

T = 4ma^2/\pi\hbar

. That is:

\Psi(x, T) = \Psi(x, 0)

for any state (not just a stationary state). (b) What is the classical revival time, for a particle of energy

E

bouncing back and forth between the walls? (c) For what energy are the two revival times equal?