Teaching Quantum Mechanics with PhET Simulations
Sam McKagan, Katherine Perkins, Wendy Adams, Danielle Harlow, Michael Dubson, Chris Malley, Sam Reid, Ron
LeMaster, Carl Wieman
University of Colorado at Boulder
http://phet.colorado.edu → Simulations → Quantum Phenomena
QM Sims
PhET Project Overview
The Physics Education Technology (PhET) Project is an ongoing effort to create a suite of interactive simulations and
related education resources that aid in the teaching and
learning of physics.
•Elaborate Java- and Flash-based simulations
•Support for educators and students with resources for both teaching
and learning with these simulations
•Developed using the results of education research and feedback from
educators
•Research to formally assess their influence on student learning and
attitudes in a variety of settings
•A large number of simulations exist and are being used in introductory
physics courses around the country
•Can be used in lecture demonstrations, recitation activities, or
homework assignments
•All PhET simulations are free and available at http://phet.colorado.edu
Addressing Common Student Difficulties
Examples:
New simulations in QM:
•Allow students to explore and construct
understanding of:
•Fundamental principles of Quantum
Mechanics
•Key ideas in historical experiments
•Quantum principles underlying
everyday life applications.
•Provide visual representations of abstract
concepts and microscopic processes that
cannot be directly observed
•Help students to build mental models of
phenomena that are often difficult to
understand.
•We found that after classroom instruction on the Davisson Germer experiment, many
students viewed the electrons as particles that happened to bounce off at certain angles
for some reason they could not understand. The simulation helped them understand
how the wave nature of light explained the results.
•Many students confuse wave function and energy as a result of the common practice
of drawing them on the same graph. Our simulations always display them separately.
•Students may be misled by static representations of the real part of the wave function
into thinking this is all there is. Our animated representations of the real part,
imaginary part, and magnitude help students grasp the full complex time-dependent
wave function in an intuitive, rather than mathematical way.
•Many non-PhET QM simulations use phase color as the primary representation for
complex wave functions. We have found that students cannot understand this
representation without extensive instruction. Our sims use other representations that
are easy for students to understand, with phase color as an advanced option.
PhET simulations in Quantum Mechanics
Fundamental Principles
ANIMATION
Watch electron waves
tunnel through barriers
See how photon
behaves as a wave as it
travels through space,
and a particle when it
hits the screen.
Quantum Tunneling
Applications
Classic Experiments
VISUALIZATION
Visualize not just the interference
pattern on the screen, but the
process that creates this pattern.
INTERACTION
CONTEXT
Change the
spacing and
radius of atoms
Find the tumor.
Davisson Germer:
Electron
Diffraction
Quantum Wave
Interference
Semiconductors
Visualize phenomena that you can’t
observe directly, such as atomic
excitations, electrons, and photons
Quantum Bound States
Photoelectric Effect
Fire the
photon gun
Directly manipulate potential with
drag handles and get instant
feedback on how this changes
energy levels and wave functions
See electrons
ejected from plate
with varying
speeds. Watch
them speed up or
slow down when
voltage is applied.
Invite to
interact
PhET is Free!
See time evolution of
wave functions
Discharge Lamps
Grab the
semiconductors
and put them in
the circuit
Lasers
Nuclear Physics
Band Structure
Visit the PhET Booth
Play with the sims
Use them this fall
New sims coming soon…
Use the sims as…
• an effective means of communicating the instructors’ visual
model to the students.
• a means for interactive engagement within class using the
Peer Instruction model with simulation-centered concept tests
or interactive lecture demos.
• a complementary learning-support tool for classroom demos.
• a short pre-class activity to prepare students for class.
Stern-Gerlach Experiment
The Hydrogen Atom
Optical Tweezers
…and more!
View light as photons or waves. Compare
and contrast these representations to get a
complete picture.
Student Responses to Quantum Sims
Teaching with PhET simulations
In-Class/Lecture
Configure your
atom’s energy
levels
Laser explodes if
it builds up too
much power.
You can download
sims & activities from
the PhET website!
Set up a chain reaction
Sample Concept Test
Simplified MRI
See electrons
jump energy
levels.
See electron
waves diffract
off atoms
Double Wells and
Covalent Bonding
Conductivity
Homework
Use the sims as…
• a method to promote active thinking with inquiry-based exercises designed
around the simulations.
• an alternative to or supplement for traditional introductory physics labs.
Photoelectric Effect
Sample Homework Problems
Lasers:
Student Responses:
Discharge Lamps
“Great sims, I can't imagine QM without them.”
“The simulations were crucial in the learning process.”
“The simulations were the best part of class, they practically answer physics questions all by
themselves. I would recommend continuing to develop these and add more. Without these I think I
would have been lost in the course.”
“I definitely not only enjoyed the simulations, but I'd go as far to say that the simulations taught me
the most about the course because I could really visualize the inner workings of the physics
processes that we going on.”
“I thought the simulations were great. It helped me to gain intuition about the topic. This is
especially useful in quantum mechanics where
Ranked one of the most useful aspects
it is not normally possible to directly observe
the described phenomena.”
of the course on end of term survey:
How useful were the following for your
“The photon ray gun I first saw in lecture and
learning? (1 – not useful, 2 – a little, 3 –
that was very important to understanding the
some, 4 – a fair amount, 5 – a great deal)
spread out nature of photons. I used the laser
simulation on my own first and had to play
with it to get it to lase, which was a good
learning experience.”
Instructors observed
that most students did
not know the correct
answer initially, but
many were able to
figure it out through
discussion. Graphs that
students drew, before
seeing multiple choice
options, closely
matched given options.
“This is what really clarified the difference
between P and N-type and to figure out what
orientation/arrangement is required for a LED
to work.”
“I related to this, for my mother has brain
cancer. She has MRIs frequently as you could
imagine. Now I know what is really going on
every time she has one done.”
Quantum Wave Interference
posted lecture notes:
the lecture period:
the homework:
the simulations:
posted homework solutions:
studying for exams:
problem solving sessions:
the textbook:
4.3
4.2
4.1
4.0
3.8
3.7
3.5
3.2
Acknowledgements
The authors thank the Hewlett Foundation, NSF, and the Kavli Operating Institute
for providing the support for the PhET Project. We also thank all the members of the
PhET Team and the Physics Education Research at Colorado group (PER@C).