A Modern Approach to Quantum Mechanics · Problem 9.16

Bound States of Central Potentials — John S. Townsend

Physics — Quantum Mechanics · spherical-harmonics-lowering-operator

Problem

(a) Obtain

Y_{1,0}

by application of the lowering operator in (9.142) to

Y_{1,1}

. (b) By direct application of the operator

\hat{L}^2

in position space [see (9.129)], verify that

Y_{1,1}

is an eigenfunction with eigenvalue

2\hbar^2