Introduction to Quantum Mechanics · Problem 4.8

Quantum Mechanics in Three Dimensions — David J. Griffiths

Physics — Quantum Mechanics · legendre_polynomial_orthonormality

Problem

Starting from the Rodrigues formula, derive the orthonormality condition for Legendre polynomials:

\int_{-1}^{1} P_\ell(x) P_{\ell'}(x)\, dx = \left(\frac{2}{2\ell + 1}\right) \delta_{\ell\ell'}. \qquad (4.34)

Hint: Use integration by parts.