Here we have the explanation and animation files (movies) for the PHYS181 course I taught in the spring of 2012.
First is a simple computation of the single-slit diffraction pattern. The point is to see under what limits the usual diffraction formula holds and how the pattern evolves from diffraction (far-field, narrow slit, etc.) to a geometrical “shadow” for a wide slit where diffraction effects are washed out. A PDF file single_slit.pdf has the explanations and figures and the matlab code that does the computations is single_slit.m.
The remainder of this page has the animations for time evolution of wave functions in one dimensions for a few simple cases. See the phys181qmREADME.pdf file for details. The actual matlab code I used to generate the movie frames are also provided for your perusal and/or experimentation (the “.m” files).
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A Gaussian wave packet bouncing around in an infinite well (particle in a box) |
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A Gaussian wave packet in a finite well bouncing around |
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A Gaussian wave packet in a harmonic potential bouncing around. Shows perfect recurrence after one period. |
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A Gaussian wave packet with a relatively wide initial width evolves in time (shows weak dispersion) |
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A Gaussian wave packet with a relatively narrow initial width evolves in time (shows strong dispersion) |
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A Gaussian wave packet is launched at a rectangular barrier and suffers reflection and transmission (shows tunneling). |
Matlab codes generating these animations: infinite_well.m , finite_well.m , qho.m , free_particle.m , tunneling.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 recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).”