Physics 3220 Quantum Animations
The following animations are given as Mathematica Notebooks (with extension .ma). They can be viewed by any viewer that has either a full working version of Mathematica on any platform, or a working version of the Mathread freeware viewing program that is available for the Macintosh, Windows PC, and NeXT environments. You can find the PC version to download here: mathrdr.exe . To obtain a reader for one of the other platforms, you should visit the following page: MathSource. Once you have the reader, and have downloaded a particular animation to your favorite platform, you can open the animation and select the desired graphics to animate, after which you should click on Graphics|Animation.
The scattering off of a double potential barrier is depicted in the following three animations, which show the probability distribution for finding a quantum mechanical particle of mass m at position x. Each of these animations refers to scattering of a particle by a potential given by:
V(x)=V0, for |a|<|x|<|b|, and V(x)=0 elsewhere. These results were obtained in a system of units for which m=1=hbar=a, and V=2=b.
Potential Energy versus position x, V(x)
Animation 1, Nonresonant energy, E=0.20 (e20.ma). Notice that there is almost complete reflection of the incident probability wavepacket, which is in accord with our expectations based on Newtonian mechanics.
Animation 2, Higher, resonant energy, E=0.52 (e52.ma). Notice the dramatically enhanced probability for the particle to be transmitted through the barriers, in a regime where classical mechanics would give zero transmission probability.
Animation 3, Still higher, but nonresonant energy, E=1.00 (e100.ma). Notice that despite the fact that the particle has higher energy than in either Animations 1 or 2, it is again reflected with almost 100% efficiency, as expected from classical physics. This shows that the very large transmission probability found in Animation 2 is not a consequence merely of the higher energy compared to Animation 1, but rather it is because the energy was "tuned" in Animation 2 to a scattering resonance - a quasi-bound state energy of the particle in the inner potential well.
If you want a shorter download and can decompress a gzipped file, the above three Mathematica notebooks can be found in:
Animation 1, e20.ma.gz |
Animation 2, e52.ma.gz |
Animation 3, e100.ma.gz
These animations have been developed by Stephanie Staley and Chris H. Greene, Copyright (c) 1995.