AP 439 files, animations, and explanations

Here we have the animation files (movies) for the APHY439 course. They show the time evolution of wave functions in one dimensions for a few simple cases.  The actual matlab code I used to generate the movie frames are also provided and the end for your perusal and/or experimentation (the “.m” files).
 
AP439README.pdf : PDF file with explanations of movies and physical setup
 

Particle in a box (infinite square well)

Gaussian centered mid box with zero average momentum
Gaussian centered mid box with mean positive momentum
Square wave function centered mid box with zero mean momentum
An infinite well problem where the initial starting point is an eigenstate, here the n=2 state of the well.  The time evolution is quite dull — this is meant to illustrate how eigenstate show no real time evolution. 
An infinite well problem where the initial starting point is the n=2 eigenstate cut off in the left half (i.e., not an eigenstate in fact).  Show actual time evolution compared to the case above!

 

Quantum Harmonic oscillator

Gaussian centered at x=0 with positive average momentum
Ground-state wave function translated to xi=7, i.e. a coherent state

 

Free particle

Gaussian centered at x=0, no momentum
Gaussian centered at x=0, positive momentum
Square wave initial function centered at x=0, no momentum
Square wave function centered at x=0, positive momentum
 

Potential scattering 

The potential well is square, extends from -a/2 to a/2 and has total area -alpha under it (i.e. its value is -alpha/a).
Potential well with a single bound state and incoming low energy packet: a=0.5, alpha=2, Gaussian packet sigma=10
Single bound state, medium energy packet: alpha=2, a=0.5, sigma=4
Single bound state, medium energy packet but narrower packet: alpha=2, a=0.5, sigma=2
 Potential with bound state, packet with wide energy spread: sigma=1, alpha=2, a=0.5, initial momentum k0=1
Potential with multiple bound states with low energy packet incoming: sigma=10, alpha=11, a=10 (this is a wide potential well).
 
Matlab codes generating these animations: particle_in_box.mqsho.mfree_particle.mpotential_scattering.m
 
”This material is based upon work supported by the National Science Foundation under Grants MRSEC DMR-0520495 and DMR-0808665.  Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).”