Table of spherical harmonics


This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree = 10. Some of these formulas give the "Cartesian" version. This assumes x, y, z, and r are related to and through the usual spherical-to-Cartesian coordinate transformation:

Spherical harmonics

\ell = 0

\ell = 1

\ell = 2

\ell = 3

\ell = 4

\ell = 5

\ell = 6

\ell = 7

\ell = 8

\ell = 9

\ell = 10

Real spherical harmonics

For each real spherical harmonic, the corresponding atomic orbital symbol is reported as well.

\ell = 0

\ell = 1

\ell = 2

\ell = 3

\ell = 4