pz

We start by defining the  p orbitals

r3dpz[theta_ , phi_ ] := Abs[ Cos[ theta] ]
r3dpy[theta_ , phi_ ] := Abs[ Sin[ theta ] Sin[ phi ] ]
r3dpx[theta_ , phi_ ] := Abs[ Sin[ theta ] Cos[ phi ] ]

To plot the pz orbital in a 3-d space we consider a fixed radius and the orientation given by (Theta, Phi).  The wave funcion amplitud for the orientation is given by: pz, py, pz orbitals, which are related to the probability of finding the electron in such orientation.  The following command projects the probability amplitud in 3-d

ParametricPlot3D[
{
  r3dpz[theta , phi ] Sin[ theta ] Cos[ phi ],
  r3dpz[theta , phi ] Sin[ theta ] Sin[ phi ],
  r3dpz[theta , phi ] Cos[ theta ]
},
{theta, 0, Pi },
{phi, -Pi ,  Pi},
ViewPoint->{4.000,4.000, 1.530},
Boxed -> False,
AspectRatio -> Automatic
                ];

The distance from the origin to any point on the surface is related to the probability of finding the electron in such orientation defined by Theta and Phi.

The square of the orbital is propotional to the probability of finding the electron in the orientation defined by Theta and Phi

Created by Mathematica  (September 7, 2006)