Having had a first course in undergraduate quantum mechanics I found Manuel Joffre?s wave mechanics physlets to be at most supplementary in nature but at the same time rather enlightening. The wave-particle duality physlet provides a simulation of the well known double slit experiment. The simulation provides two windows. The first window serves as a backdrop revealing the interference pattern that characterizes the wave behavior of particles passing through a two slit barrier. The second window serves as a histogram for each shot registered at a particular channel/detector on the backdrop. The author does well in asking the user to make qualitative and quantitative assessments as to why the relative noise in the per channel histogram decreases with sample size. This really forces the all important notion of statistical procedure associated with quantum mechanics.
In this double slit simulation, the user may vary two aspects of the experiment: the rate at which particles are fired and the number of fringes to be observed. Some comments might be in order concerning the option for fringe variation. When a double slit experiment is performed in the laboratory, there are certain parameters that must be varied to produce a different number of fringes. Having presented the option for fringe variation in the simulation, it seems natural to provide some instructional comments as to why fringe variation is possible and how it relates to wave theory and experiment.
In the second physlet, Joffre presents a simulation of the propagation of a free wave packet in a dispersive medium. The simulation provides an excellent visualization of the spreading /dispersion of a wavepacket as it propagates through space. As in the double slit simulation,
this simulation has a dual window presentation. The simulation allows the user to toggle between two different representations of the same wave packet as it moves and disperses through space. The first representation is the probability density associated with the wave packet in configuration space. The second representation is the actual physical wave packet itself or the real part of the packets wave function. By toggling between these two representations the user may develop some intuition as to how a probability density in configuration space relates to the physical propagation/dispersion of a wave packet in space. In short, this dual representation offers an excellent opportunity to develop some physical interpretation of a probability density. The author offers some instructional comments concerning the spreading of the wave packet and its probability density in momentum space. While the comments are instructive, perhaps a third representation of the wave packet in momentum space would be most enlightening. In conjunction with the configuration space and real/physical representations , a third representation in momentum space might allow the user to form a more complete picture of the motion of a wave packet and its associated probability densities.
The next of Joffre?s simulations presents a particle of fixed energy relative to potential steps and barriers of various energies. In the case of potential steps the user may vary the step potential and then observe the differences in transmission and reflection probabilities. Probability densities are plotted versus position. The simulation is extremely effective in conveying the idea of how step potentials of various energies affect probabilities of reflection/transmission. In the case of finite potential barriers,
the user may vary only the barrier width and not the barrier height. This is somewhat unfortunate as both barrier height and barrier width determine transmission/reflection probabilities. This dual dependence on height and width seems to be obscured by restricting the users ability to vary only barrier width.
The final simulation in this wave mechanics applet brings us back tothe laboratory with an interactive demonstration of the scanning tunneling microscope (STM). Here, the user traces out the surface of some sample by varying the height of the STM. As the STM traverses across the surface of the sample, electrons tunnel into the microscope?s tip through a Coulomb potential due to the sample?s nuclei and thus generate a measurable current. The user has the task of keeping the measured current constant by varying the height of the STM as it moves across the sample. The interactive nature of this simulation gives the user a good idea of how an STM works and what it measures. What seems to be lacking here are some contextual comments on how the measurements might be interpreted and the overall purpose and usefulness of the STM. More on the STM, however, may by be found in the last segment of this wave mechanics applet. This last segment also contains some interesting biographical sketches of quantum mechanics? most well known pioneers.
In summary, the simulations in this wave mechanics applet do much to enhance the users intuition of some key concepts in quantum mechanics. The dual representations in both the double slit and wave packet simulations are most revealing in their presentation of probability densities, a cornerstone of quantum mechanics. To make a final criticism,
the author might have done better in providing some textual instruction; the simulations seem to have been presented in a sort of vacuum where key concepts might be missed for lack of textual underscore.