Principles of Quantum Mechanics · Problem 11.4.2

Rotational Invariance and Angular Momentum — R. Shankar

Physics — Quantum Mechanics · parity-invariance

Problem

A particle is in a potential

V(x) = V_0 \sin(2\pi x/a)

which is invariant under the translations

x \to x + ma

, where

m

is an integer. Is momentum conserved? Why not?