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Applets for quantum mechanics
This set of applets features illustrations of quantum mechanics through interactive animations in the following domains : Young interference fringes  wavepacket propagation  linear superposition of eigenstates (including coherent states of the harmonic oscillator)  nuclear magnetic resonance.
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Son Kim (Student)
Chris Wolowiec (Student)
Joffre?s wave mechanics physlets to be at most supplementary in nature but at
the same time rather enlightening. The waveparticle 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.
Franziska vonHerrath (Student)
aspects of quantum mechanics. With their changeable conditions, the applets
inspire great curiosity for the layman to inquire more in depth about the
presented topics as well as clarification for the a little more advanced physics
student. In either case, the applets invite the user to spend ample time with
the concepts.The applets are not only very helpful and sound, but also an
aesthetically pleasing supplement to any Quantum Mechanics/Modern Physics book.
Minor technical flaws overal do not distract from the site's easy to use,
instructing applets.
Wave/Particle Duality in Quantum Mechanics
This site superbly visualizes the Young slit experiment. The posed question
about the reason for the decrease in noise the when more particles have hit the
screen guides the reader in the right direction to think of the experiment in a
statistical manner.
Propagation of a Free Wavepacket
The otherwise difficult to envision propagation and successive spreading of a
wavepacket is playfully illustrated here. The only improvement suggestions I
have are
1) To enlarge the graph in which the waves are spreading. This way the waves of
width 1 and 2 would more clearly show signs of spreading by the time they reach
the graph's end in both the probability density as well as in the real part of
the wave function.
2) To include the wavepacket's propagation in momentum space as it is so tightly
related to configuration space.
Propagation of a NonMinimal Wavepacket
This illustration is an excellent follow up to the previous applet. Not all
wavepackets start propagation from their minimum size. The nonminimal
wavepacket first contracts in configuration space as the waves with higher
frequencies at the trailing edge "catch up" to the bulk of the wave and then
spread ahead of the rest.
Steps and barriers
This applet smoothly visualized a gaussian wavepacket hitting a step potential
under various conditions. The reflection, interference and transmission are
evident and well executed. The user really benefits from the changeability of
the energy of the step potential. There is one thing that demands change for the
text to be physically sound: The second paragraph should read "When the step
height is less or smaller ?" It would also be nice to see what happens when a
wavepacket hits a finite barrier of step height less than its particle energy.
Scanning Tunneling Microscope
This applet is a fun and thoughtful addition to the previous visualizations as
it provides a bridge from theoretical to measurable physics. I suggest
explaining what is meant by the "sample." The electric green color made me think
of GAK, which the sample is not.
Technical Remarks:
flawless reading. A better compromise between tex box size and applet size
could also be found. When manipulating an applet would be moe helpful to be able
to read the whole featured explanation text rather than merely one sentence at
a time.
Ian Clark (Student)
visual elucidation and thus inspiration to the novice quantum mechanic. It is
easy to feel like quantum mechanics is a vast collection of unrelated
mathematical abstractions when one first embarks on the timehonored set of
introductory wave mechanics problems (the particle in a box, particle incident
on a step potential, harmonic oscillator etc?). This site illustrates every
introductory wave mechanics problem I had previously encountered and several I
had not. While the lack of associated text and derivation makes this site
unsuitable as a stand alone educational tool it did give many of these problems,
which were heretofore vague and abstract, a more visual and concrete
significance, and a sense of coherence which I found to be quite appealing. The
material presented on this site is primarily at or above my current level of
competence in the field of wave mechanics and partial differential equations,
but with that disclaimer, I could find no flaws in the material presented.
My favorite applet was the particle incident on a step potential barrier. If
memory serves most texts put forth a similar problem to describe the
transmission probability in which the particle is described by a completely
delocalised wave function (&Delta x = infinity). In the applet the particle is
described by a function with finite uncertainties in momentum and position. I
found that the treatment given in the applet provided a more intuitive sense of
transmission of a particle through a barrier, and when time permits I would like
to work through the problem for myself. I also enjoyed the applet depicting
the double potential well, but further rumination is needed before I can make
any reasonably intelligent commentary on it.
In summation I would say that this site is the first to have truly convinced me
that Java can play an important role in the teaching of physics, and I intend to
return to it to further my own understanding of the subject. My
congratulations are extended to its authors.
Technical Remarks:
done: plots are clearly labeled and easy to read, all functions are
straightforward and easy to use, and the presentation is professional and
aesthetically appealing. The only drawbacks I could identify were a handful of
typographical errors and the daunting size of the Java applets. The average
applet size appeared to be in the neighborhood of 150k, which produced a 10 to
30 second delay on the university computers. I shudder to think how long they
would have taken me to load through the 28.8 modem on my home computer
Donald Hornback (Student)
on wave mechanics. I am a junior undergraduate physics major who has completed
a course in modern physics, and I have also been exposed to material generally
covered in the first few chapters of an undergraduate quantum mechanics text.
My response to this site is extremely positive. The animations concerning both
the wavepacket propagation and the steps and barriers clearly illustrate
concepts that I had not yet been able to clearly visualize. When I take a
quantum mechanics course in the fall and will be more actively studying the
mathematics of the subject, I intend on returning to this site for a
betterinformed pass at the wave mechanics applets, as well as the additional
material of the site. Comments concerning the specific material reviewed
follow:
Waveparticle duality in a Young slit experiment: I found the animation an
excellent representation of the particlewave slit experiment and was reminded
of Feynman scratching out probability curves on his blackboard. I cranked up
the rate of the ?lumps? being fired and watched as the curves on the histogram
smoothed out to the nearly continuous distributions expected. Simple and very
nice.
Propagation of a wave packet: Having scratched my head more than once trying to
visualize a ?wavepacket propagating through space?, this applet and some
rereading of textbook material helped me to make some headway on this subject,
at least twodimensionally. I liked that one could specify to watch either the
absolute square of the wave function or the real part of the wave function.
That the parts of the wavepacket with the greater momentum will propagate
faster causing spreading of the wavepacket makes sense when you can watch it
happen. I like the option of varying the width (from .5, 1,2) of the
wavepacket, assuming that the numbers .5,1,2 correspond to relative widths.
This variable ?width? isnice to show that the more localized the packet is
initially, the quicker it spreads out in space due to the correlation of
increased localization and increased uncertainty in momentum. That the parts of
the packet with larger momentums would propagate with larger velocities is
nicely seen, though I would prefer to see the animation progress a bit longer
than it does. Quibbles.
Propagation of nonminimal wavepackets: Just a variation on the previous,
excellent wavepacket applet. The wavepacket localizes and then spreads due,
as I have read, to the different initial configuration of momenta in the packet.
I have also read that outside measurements will collapse a wavepacket, only
for the wavepacket to then spread out or ?grow? with time, collapsing again at
each additional measurement. How exactly is this phenomenon related to the
nonminimal wavepacket portrayed in this applet?
Steps and Barriers: This is the section for which I have the least exposure and
understanding. Again, the animation of quantum tunneling appears to be a
wonderful treatment of the subject, but since I am not versed in the mathematics
of the phenomenon, in my eyes it still smacks of witchcraft, something I hope
that will pass with further exposure. Varying the step size to watch the
relative amount of the wave reflected and transmitted is a very instructive
exercise, and I look to revisit this applet in the near future when I am better
armed.
Scanning tunneling microscope: Our excellent electronics instructor here at
Humboldt State has spoke on this topic a few times, and this applet reflects
exactly what I have already learned on the subject (on a relatively qualitative
level). The applet provides a nice, fairly qualitative look at the subject, and
the interactive part is instructivecalling it a game might be a bit of a
stretch.
Technical Remarks:
sizable, the load time on my 56K modem was only about ten seconds?well worth the
brief wait. There were a few typos noticed, and the brief encroachment of
French on the English site (e.g. barriere). The author has obviously paid great
attention to detail throughout, both in the programming and in the physics. I
offer only my compliments.
Lawrence Sweet (Student)
Mechanics.
The physical observables demonstrated in the applets are well chosen and allow
for rapid serial imprinting of the basics of the theory. I believe that student
brain time devoted to insufficient mental models of QM is better served by
something like these applets which allow the mind to jump an abstraction layer
conceptually.
This is a good, nonmathematical starting point for QM.
Technical Remarks:
new some new physics I had not known about.
The only thing I could think to improve would be to specify in the wave packet
applet whether or not the wave packet is the minimum uncertainty (Gaussian).
Sheila Dodson (Student)
of the physicist. For it is our imagination and physical intuition that lead us
to new discoveries. Web pages such as this one help students see, and
therefore be able to better imagine the world of quantum mechanics.
The beauty of java applets is their ability to show experiments that are
difficult, or even impossible to reproduce in the class room. For example, the
applet displaying the spreading of the wave packet shows students something they
could never see in real life by showing not only the way the packet spreads
over time, but the real AND IMAGINARY components of the wave. Illustrations
such as these simultaneously help the student understand the situations quantum
mechanics deal with, and hopefully spark their imagination as well.
The customizable nature of the applets transforms the simulations into virtual
experiments, allowing the students to put their new knowledge to work. They can
gain a wonderfull intuition about the various systems by playing with the
different variables.
With all this in mind, it is important to remember that the applets alone
cannot do the full job of teaching quantum mechanics. No matter how interactive
they are, they are still limited to the boundaries of their program. As a
result they can never answer all the questions and address all the concerns of
prospective students. They must retain their position in life as a teaching
tool, not a teacher.
Technical Remarks:
text and view the applet at the same time. Given the wonderfull job the
programmers did putting together these applets, this is definately negligable,
yet an annoying feature of this site. On the other hand I must comment that the
translation from French to English was done quite well, with the exception of a
few typos
Sorel Reisman (Faculty)