What to "expect" from quantum mechanics?

How can we use the framework of quantum mechanics to tell us something useful to chemists? The expectation value and the probability density are the keys. The eigenfunctions of the Hamiltonian are an orthonormal set. We graphed the probability density and wavefunctions for the particle in the box. We noticed that as n increased, the probabilty profile appeared more classical - a manifestation of the Bohr Correspondance Principle.

MP3 podcast
webcast
Mathematica notebook to plot the wavefunctions and probality densities