Quantum Wave Packet Evolution in an Infinite Square Well

The infinite square well potential is \(V=0\) for \(0\lt x\lt 1\) in infinite otherwise. The initial wave function is described by

\[ \Psi(x, 0) = Ae^{-a(x - x_0)^2}e^{ikx} \]

where \(a\) controls the width of the wave packet, \(x_0\) is the initial position of the wave packet's center, and \(k\) relates to the initial momentum of the wave packet. Below show the time-evolution of \(|\Psi|^2\) where the color indicate the argument of \(\Psi\)

a: 100
x0: 0.5
k: 30
Scale: 5.0