  We compare the classical and quantum mechanical position-space probability
densities for a particle in an asymmetric infinite well. In an idealized system
with a discontinuous step in the middle of the well, the classical and quantum
probability distributions agree fairly well, even for relatively small quantum
numbers, except for anomalous cases which are due to the unphysical nature of
the potential. We are able to derive upper and lower bounds on the differences
between the quantum and classical results. We also qualitatively discuss the
momentum-space probability densities for this system using intuitive ideas
about how much time a classical particle spends in various parts of the well.
This system provides an excellent example of a non-trivial, but tractable,
quantum mechanical bound state problem where the correlations between the
amplitude and curvature of quantum mechanical wavefunctions can be easily
compared to classical intuition about particle motion, with quantitative
success, but also warning of possible surprises in non-physical limiting cases.
