Introduction to Quantum Mechanics · Problem 4.25

Quantum Mechanics in Three Dimensions — David J. Griffiths

Physics — Quantum Mechanics · spherical_harmonics

Problem

(a) What is L+YℓℓL_+ Y_\ell^\ell? (No calculation allowed!) (b) Use the result of (a), together with Equation 4.130 and the fact that LzYℓℓ=ℏℓYℓℓL_z Y_\ell^\ell = \hbar \ell Y_\ell^\ell, to determine Yℓℓ(θ,ϕ)Y_\ell^\ell(\theta, \phi), up to a normalization constant. (c) Determine the normalization constant by direct integration. Compare your final answer to what you got in Problem 4.7.

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