Here are some renderings of the real ('Cartesian') representations of the atomic orbitals of a one electron atom. The surfaces represent a contour of equal probability amplitude. The different colors of the lobes represent different phases (signs) of the wavefunctions in those regions.

The 'natural'' solution to the angular part of the Schroedinger Eqn for the one electron atom is complex for non-zero angular momentum projection on the space-fixed axis. The natural functions for the description of a system with spherical symmetry are the Spherical Harmonics

Enjoy! [I didn't label the x, y, and z coordinates, can you?]

L=0

L=1

The 2p_{x} orbital

The 2p_{y} orbital

The 2p_{z} orbital

The 3p_{x} orbital

The 3p_{y} orbital

The 3p_{z} orbital

The 4p_{x} orbital

The 4p_{y} orbital

The 4p_{z} orbital

L=2

The 3d_{z}^{2}
orbital

The 3d_{yz} orbital

The 3d_{xz} orbital

The 3d_{xy} orbital

The 3d_{x}2_{-y}2
orbital

The 4d_{z}^{2}
orbital

The 4d_{yz} orbital

The 4d_{xy} orbital

The 4d_{xz} orbital

The 4d_{x}2_{-y}2
orbital

L=3

The 4f_{z}3 orbital

The 4f_{xz}2 orbital

The 4f_{yz}2 orbital

The 4f_{xyz} orbital

The 4f_{z(x}2_{-y}2_{)}
orbital

The 4f_{x(x}2_{-3y}2_{)}
orbital

The 4f_{y(3x}2_{-y}2_{)}
orbital

These renderings have been provided by Dr. Yue-Ling Wong
(without her knowledge, actually)

P. J. Brucat || University of Florida || Chemistry Dept