Physlet Illustration: Hydrogen Atom Wavefunctions
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In this simulation, several views of the quantum mechanical hydrogen atom are shown.  The plot in the upper left is a polar plot showing how the wavefunction depends upon angle.  The plot in the upper right shows the radial (distance) dependence.  And the plot in the lower left illustrates the electron density.  The text boxes in the lower right allow the user to change the quantum numbers for this hydrogen atom.  How does the probability of finding the electron in a particular location depend on the quantum numbers?

Hints:

  1. What rules for picking quantum numbers must be followed?
  2. Which combinations of the quantum numbers results in spherically symmetric patterns?  Which produce lobes of various kinds?
  3. For quantum numbers which produce spherically symmetric distributions, what affect does the principle quantum number have on the radial distribution?
  4. For a fixed principle quantum number what affect does changing the angular momentum quantum and magnetic quantum numbers have?  You will want to use a sufficiently large principle quantum number to allow some experimentation. 

Reference

See Walker, Sections 31-5

Illustration written by Dan Boye and Modified by Chuck Niederriter