Table of spherical harmonics

This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree ℓ {displaystyle ell } = 10. Some of these formulas give the 'Cartesian' version. This assumes x, y, z, and r are related to θ {displaystyle heta } and φ {displaystyle varphi ,} through the usual spherical-to-Cartesian coordinate transformation: This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree ℓ {displaystyle ell } = 10. Some of these formulas give the 'Cartesian' version. This assumes x, y, z, and r are related to θ {displaystyle heta } and φ {displaystyle varphi ,} through the usual spherical-to-Cartesian coordinate transformation: For each real spherical harmonic, the corresponding atomic orbital symbol (s, p, d, f, g) is reported as well.