Quantum Mechanics (1) · Problem 5.5

Rotations and angular momentum

Physics — Quantum Mechanics · haar-measure-invariance

Problem

Show that the Haar measure is both left- and right-invariant. That is,

\mu(S) = \mu(SR_0) = \mu(R_0 S)

for all

R_0 \in O^+(3)

and for all measurable sets

S \subset O^+(3)