Time-dependent Infinite Square Well

Description

Shown is the time-dependent wave function for a particle in an infinite square well of length a=2.   The wave function evolves with time according to the TDSE.  You may change the state by choosing an n. 

Questions

1. For n=1, what does a time of t = 1 correspond to?  Why?
2. For n=1, what then does the color of the wave function at t=0, 0.25, 0.5, 0.75, and 1 correspond to?

Answers

1.  It is the time it takes for the wave function to "revive".   In other words, it is the time for the wave function to undergo a phase change of 2p.  Specifically,  this time is the inverse frequency of the time-dependent infinite square well ground state.

2. t=0=blue=real and positive.

   t=0.25=light green=imaginary and negative.

   t=0.5=goldish=real and negative.

   t=0.75=magenta=imaginary and positive.

   t=1=blue=real and positive.

Note that the time-evolution of the wave function is governed by exp(-iE_nt / hbar).  As a consequence,  the rotation in the complex plane is clockwise rather than counterclockwise.

Required Resources

Jar files: DataGraph4_.jar,  Filters4_.jar, STools4.jar

Credits

Script by Mario Belloni.
Questions by Mario Belloni.
Java applets by Wolfgang Christian.