Page 8 - Physlets and Open Source Physics for Quantum Mechanics:

Evolution of a Quantum Wave Packet: Short- and Long-term Behavior in the Infinite Well

Figure 8: The color strip that serves as a conversion between the phase of the
wave function and the color representation of the phase used in the animations.

In the following examples we will focus on the time evolution of Gaussian wave packets in the
infinite square well. In time-dependent quantum mechanics it is necessary to describe the wave
function in terms of complex (real and imaginary) functions. In order to animate these time-
dependent functions, we use an amplitude and phase representation of the wave function. The
amplitude is drawn centered on the y-axis and is the height of the envelope shown from top to
bottom. The phase, or phase angle, of the wave function is shown as color and we often show a
color-conversion image, as in Figure 8 to help students determine the phase of the wave function.

Figure 9: A quantum wave packet in the infinite square well visualized with the
program QMSuperpositionProbabilityApp. The wave packet is shown at t = 0,
T cl/4, T cl/2, 3T cl/4, and T cl, respectively (T rev is set to 1). During the classical
period, the wave packet has begun to noticeably spread. In the top panels the
wave function is shown in phase as color representation and in the bottom
panels the probability density is shown.