Wigner quasi-probability distribution for the infinite square well: Energy eigenstates and time-dependent wave packets

We calculate and visualize the Wigner quasi-probability distribution for the position and momentum, P _W ⁽ⁿ⁾(x, p), for the energy eigenstates of the infinite square well. We evaluate the time-dependent Wigner distribution, P _w(x,p;t), for Gaussian wave packet solutions of this system, and illustrate the short-term semi-classical time dependence and the longer-term revival and fractional revival behavior. Our results indicate how the Wigner distribution can be used to examine the highly correlated dynamical position-momentum structure of quantum states. In particular, this tool provides an excellent way of demonstrating the patterns of highly correlated Schrödinger-cat-like "mini-packets" which appear at fractional multiples of the exact revival time.