042-Fundamentals-of-Physics-II-Electromagnetism-Optics-and-Quantum-Mechanics-R.-Shankar-Edisi-1-2016 · Problem 22.1

States of Definite Energy

Physics — Shankar · energy-measurement-box-sketching

Problem

Sketch the first four wave functions

\psi_n(x)

on top of

\psi(x)

(given by Eqns.\ 22.82--22.83) and try to see why

P(n)

vanishes whenever

n

is a multiple of 4, given that

P(n) = \frac{16}{n^2\pi^2}\sin^4\!\left[\frac{n\pi}{4}\right].