Principles of Quantum Mechanics · Problem 12.5.11

Rotational Invariance and Angular Momentum — R. Shankar

Physics — Quantum Mechanics · spherical-harmonics-derivation

Problem

Derive

Y_1^1

starting from Eq. (12.5.28) and normalize it yourself. [Remember the

(-1)^l

factor from Eq. (12.5.32).] Lower it to get

Y_1^0

and

Y_1^{-1}

and compare with Eq. (12.5.39).