Scatter plots of hydrogen-atom wavefunctions

This is a tentative project. The figures that you can link to from this page are made by choosing 2000 points at random, with a probability given by one of the hydrogen atom's wavefunctions. The resulting plots give an idea of the "shape" of the atomic wavefunctions. You can rotate them by clicking and dragging with the mouse; you can also magnify the figure by clicking and dragging vertically while holding down the "shift" key.

The points were generated in Mathematica and the interactive figures were generated using LiveGraphics3D. LiveGraphics3D is an applet (not written by me); for it to work, you need to have java enabled in your browser.

n=1

• n=1, l=0, m=0

n=2

l=0

• n=2, l=0, m=0

l=1

• n=2, l=1, m=0
• n=2, l=1, m=1 (same probability distribution as n=2, l=1, m=-1)

n=3

l=0

• n=3, l=0, m=0

l=1

• n=3, l=1, m=0
• n=3, l=1, m=1 (same probability distribution as m=-1)

l=2

• n=3, l=2, m=0
• n=3, l=2, m=1 (same probability distribution as m=-1)
• n=3, l=2, m=2 (same probability distribution as m=-2)