Quantum Physics Series:
Films 1 through 9 produced by Judah Schwartz, Harry Schey, and Abraham Goldberg. Film 10 produced by Harry Schey. Judah Schwartz, and Roy Whiddon.
All films were produced at the Education Development Center. All distributed by Education Development Center, 39 Chapel St., Newton, MA 02160.
Films 1-9 distributed by BFA Educational Media. 2211 Michigan Ave, Santa Monica, CA 90406. 16mm or S8mm, B/W. silent, computer-animated, 3 to 4 min each. 16mm Price: $20 purchase each title (EDC), $20 series rental (EDC). S8mm Price: $15.95 each (BFA).
Topic: Computer-animated films which visualize the time development of wave packets in various one-dimensional environments. All of the phenomena are described by the time-dependent Schrodinger equation. Level: Advanced undergraduate and graduate physics courses.
Quantum Physics Series is a sequence of ten computer-animated short films that illustrate a variety of phenomena in quantum mechanics. All of these films are concerned with time-dependent solutions of the one-dimensional Schrodinger equation. They are therefore suitable to undergraduate courses in quantum mechanics, but they display subtleties that will have escaped most graduate students and even many experienced physicists.
Three facets of one-dimensional quantum mechanics are covered. The first is scattering by potential wells; the sccond is propagation in a crystal; the third illustrates the statistical meaning of the wave function. Of these, the films on scattering by potentials are well-known to many physicists, but the remainder of the series was not known previously to this reviewer, or to his colleagues.
The two films, Barriers and Wells, show scattering by repulsive and attractive square-well potentials in coordinate space. What is particularly revealing here is the behavior of the wave function in the classically forbidden region. It is also very interesting to see the similarity between a wave that has insufficient energy to overcome the barrier and the familiar phenomenon of ocean waves striking a sea wall.
To explain the importance of an abrupt edge, Edge Effects show what happens when the square well is replaced by a trapezoidal well. Unfortunately, even this example still has discontinuities, and it would have been illuminating to see to what extent scattering by a truly continuous potential still leads to transient modulations of the wave packets.
Viewers can gain further insight by seeing the film devoted to scattering in momentum space. Momentum Space depicts in a very dramatic, and probably unfamiliar manner, how the scattered wave evolves in time: before the collision the incident wave packet is stationary, and then, quite suddenly, the reflected wave pops up in a totally different point in momentum space. That this merely provides a different description of the same phenomenon as the earlier film in coordinate space should serve to underline the meaning of representation in quantum mechanics.
While all the above films will certainly enhance the viewer's understanding of quantum mechanics, and leave him with a far more graphic intuition than he is likely to glean from a study of the mathematics, they do leave something to be desired. In particular, the lack of a sound track means that even an experienced quantum mechanic must remain fully alert and on his toes if he is to understand what he is seeing, and even then it is quite certain that he will have missed a number of more subtle points. Instructors using these films would be well advised to see them several times before showing them, and should also precede the showing by an explanation of what is to be seen. It would have been helpful if the films gave more quantitative information concerning the solutions that are shown. For example, in Barriers (the scattering of a wave packet by a potential barrier) the relationship between the incident momentum and the height of the barrier is given. But on the film there is no information whatsoever concerning the relationship between the incident momentum and the width of the barrier.
In the film Momentum Space several of the captions are somewhat misleading in that they describe what is shown as an event. Needless to say, the wave function does not describe a single event. This is mitigated by the fact that one of the later films nicely explains the meaning of event in quantum mechanics.
In the reviewer's opinion the outstanding films in this series are those on scattering and propagation in a crystal lattice (Kronig-Penney potential). Quite aside from their pedagogic value these films are visually very beautiful, easily on a par with visual displays occasionally shown in museums of modern art. The propagation of a wave packet in a crystal proves to have the elegance and grace of the best ballet.
Turning to more mundane matters, this sequence of films shows the propagation of a packet in a perfectly periodic crystal: Packets in a Perfect Crystal, scattering of the packet by an impurity (i.e., a narrow potential barrier at one site): Scattering from an Impurity, and reflection and refraction at crystal surface: Packets Incident on a Crystal. The latter phenomenon is shown both when the incident mean wavelength can propagate in the crystal, and when it is in a forbidden region. In the latter case there is almost total reflection and the surface effects are particularly interesting.
The final film that deserves comment concerns the statistical meaning of the wave function: Individual Events in One-Dimensional Scattering. The example chosen is again scattering by a one-dimensional barrier. What is shown is the evolution of the wave packet, and the same view also shows the stochastic distribution of actual events in an experiment with a finite number of particles. Here the explanatory material in the captions is especially inadequate, but the film is very valuable nonetheless.
To summarize: These films can be a very useful aid for an instructor who is prepared to study them carefully before showing them to his class. It is somewhat unfortunate that the labor and ingenuity that was obviously expended in creating these films was not supplemented by a relatively small effort to provide more detailed explanatory material.
[Editor's note: The S8mm films have notes with the films, the 16mm films do not. There are details about the films in:
A Goldberg, H M Schey, and J L Schwartz, Am J Phys 35, 177-186 (1967).