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)
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Gaussian centered mid box with zero average momentum |
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Gaussian centered mid box with mean positive momentum |
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Square wave function centered mid box with zero mean momentum |
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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. |
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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
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Gaussian centered at x=0 with positive average momentum |
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Ground-state wave function translated to xi=7, i.e. a coherent state |
Free particle
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Gaussian centered at x=0, no momentum |
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Gaussian centered at x=0, positive momentum |
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Square wave initial function centered at x=0, no momentum |
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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).
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Potential well with a single bound state and incoming low energy packet: a=0.5, alpha=2, Gaussian packet sigma=10 |
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Single bound state, medium energy packet: alpha=2, a=0.5, sigma=4 |
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Single bound state, medium energy packet but narrower packet: alpha=2, a=0.5, sigma=2 |
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Potential with bound state, packet with wide energy spread: sigma=1, alpha=2, a=0.5, initial momentum k0=1 |
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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.m , qsho.m , free_particle.m, potential_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).”