Teaching Quantum Mechanics with PhET SimulationsSam McKagan, Katherine Perkins, Wendy Adams, Danielle Harlow, Michael Dubson, Chris Malley, Sam Reid,

Ron LeMaster, Carl WiemanUniversity of Colorado at Boulder

The Physics Education Technology (PhET) Project is an on-going 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

PhET simulations in Quantum Mechanics

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).

PhET Project Overview

Classic Experiments

Teaching with PhET simulations

In-Class/Lecture HomeworkUse 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.

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.

INTERACTIONINTERACTIONANIMATIONANIMATION CONTEXTCONTEXT

http://phet.colorado.edu → Simulations → Quantum Phenomena

VISUALIZATIONVISUALIZATION

Set up a chain reaction

ApplicationsFundamental Principles

“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

Student Responses to Quantum Sims

Examples:

•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.

Addressing Common Student DifficultiesQM Sims

PhET is Free!

You can download sims & activities from the PhET

website!

Visit the PhET Booth

Play with the simsUse them this fall

Photoelectric EffectPhotoelectric Effect

Quantum Wave InterferenceQuantum Wave Interference

Discharge LampsDischarge Lamps

Lasers:Lasers:

Sample Homework Problems

Sample Concept Test

Acknowledgements

Ranked one of the most useful aspects of the course on end of term survey:

How useful were the following for your learning? (1 – not useful, 2 – a little, 3 –

some, 4 – a fair amount, 5 – a great deal)

posted lecture notes: 4.3

the lecture period: 4.2

the homework: 4.1

the simulations: 4.0

posted homework solutions: 3.8

studying for exams: 3.7

problem solving sessions: 3.5

the textbook: 3.2

New sims coming soon…

Stern-Gerlach ExperimentThe Hydrogen AtomOptical Tweezers

…and more!

Nuclear Physics

Photoelectric Effect

Student Responses:

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.

it is not normally possible to directly observe the described phenomena.”

“The photon ray gun I first saw in lecture and that was very important to understanding the 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.”

“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.”

Davisson Germer: Electron

Diffraction

Lasers

Semiconductors

Conductivity

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.

Fire the photon gun See electrons

ejected from plate with varying

speeds. Watch them speed up or slow down when

voltage is applied.

Visualize not just the interference pattern on the screen, but the

process that creates this pattern.

Find the tumor.

Laser explodes if it builds up too much power.

Visualize phenomena that you can’t observe directly, such as atomic

excitations, electrons, and photons

Configure your atom’s energy levels

View light as photons or waves. Compare and contrast these

representations to get a complete picture.

Simplified MRI

See electrons jump energy

levels.

Quantum Wave Interference

Quantum Tunneling

Grab the semiconductors and put them in

the circuit

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.

See electron waves diffract

off atoms

Change the spacing and

radius of atoms

Invite to interact

Directly manipulate potential with drag handles and get instant

feedback on how this changes energy levels and wave functions

See time evolution of wave functions

Quantum Bound States

Double Wells and Covalent

BondingBand

Structure

Discharge Lamps