Principles of Quantum Mechanics · Problem 12.5.9

Rotational Invariance and Angular Momentum — R. Shankar

Physics — Quantum Mechanics · angular-momentum-hermiticity

Problem

Show that

L^2

above is Hermitian in the sense

\int \psi_1^*(L^2\psi_2)\, d\Omega = \left[\int \psi_2^*(L^2\psi_1)\, d\Omega\right]^*