The Spherical Harmonics Gallery Page

is offered to you by the

Quantum Chemistry Group

Departamento de Química Física y Analítica
Universidad de Oviedo, 33006-Oviedo, Spain



Real combinations of spherical harmonics. Click on each image to see a large rendering of the same plot. The surfaces have been colored according to the value of the PHI spherical coordinate of the points.
-3 -2 -1 ml=0 1 2 3
l=0
l=1
l=2
l=3


The spherical harmonics

A spherical harmonic , , is a single-valued, continuous, bounded, complex function of the angular coordinates and . They play an important role in quantum mechanics as the eigenfunctions of the angular momentum operators and . Alternatively, the spherical harmonics are a complete basis for the irreducible representations of the infinite rotations group .

Depicting the complex functions would require four dimensions. We can represent, however, the real combinations of spherical harmonics defined as:

The creation of the images

The images have been created using tessel , a program that reads in the analytical expressions that define a parametric surface and produces a quadrilateral or triangular mesh of it. The rendering of the surfaces has been done with POV-Ray 2.2.


This document: http://web.uniovi.es/qcg/harmonics/charmonics.html
Page dates: Jan. 21, 1997 (creation), Sep. 22, 2003 (last update). Admin.: victor@carbono.quimica.uniovi.es
Copyright © 1997-2003 Víctor Luaña.