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Applets for quantum mechanics

Rating: 4 stars
Used in Course: Not used in course
Submitted by: Chris Wolowiec (Student), May 01, 2001
Comment: 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

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

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.