  After briefly reviewing the definitions of classical probability densities
for position, $P_{CL}(x)$, and for momentum, $P_{CL}(p)$, we present several
examples of classical mechanical potential systems, mostly variations on such
familiar cases as the infinite well and the uniformly accelerated particle for
which the classical distributions can be easily derived and visualized. We
focus especially on a simple potential which interpolates between the symmetric
linear potential, $V(x) = F|x|$, and the infinite well, which can illustrate,
in a mathematically straightforward way, how the divergent, $\delta$-function
classical probability density for momentum for the infinite well can be easily
seen to arise. Such examples can help students understand the quantum
mechanical momentum-space wavefunction (and its corresponding probability
density) in much the same way that other semi-classical techniques, such as the
WKB approximation, can be used to visualize position-space wavefunctions.
