We analyze the difference between classical dynamics (geometric optics
) and quantum dynamics (wave optics) by calculating the time history o
f the Wigner function for the simplest nonlinear Hamiltonians which ar
e fourth-degree polynomials in p and q. It is shown that the moments o
f the Wigner function carry important information about the state of a
system and can be used to distinguish between quasiclassical and quan
tum evolution.