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Developing and Researching PhET simulations for Teaching Quantum Mechanics
S. B. McKagan, K. K. Perkins, M. Dubson, C. Malley, S. Reid, R. LeMaster, C. E. Wieman
TL;DR
Quantum mechanics is difficult to learn because it is counterintuitive, hard to visualize, mathematically challenging, and abstract, while existing research has covered only a limited set of topics. This paper presents 18 research-based PhET quantum simulations, their development and classroom use, and evidence that they support learning while revealing student thinking about quantum mechanics.
Problem
Quantum mechanics remains difficult for students, and prior education research has focused on relatively few topics despite broader unresolved questions about learning and teaching.
Method
The paper develops and studies interactive PhET quantum simulations using research-based design principles, student interviews, classroom testing, and varied instructional contexts.
Results
Students showed strong reported and measured learning outcomes, including 83% correct reasoning versus 20% in traditional instruction on one photoelectric-effect question and 92% correct explanations on a Davisson–Germer exam question.
Takeaways & Limitations
Visualization, interactivity, context, and efficient computation can help students understand abstract and counterintuitive quantum concepts while supporting conceptual exploration.
Abstract
from arXiv · showhide
Quantum mechanics is difficult to learn because it is counterintuitive, hard to visualize, mathematically challenging, and abstract. The Physics Education Technology (PhET) Project, known for its interactive computer simulations for teaching and learning physics, now includes 18 simulations on quantum mechanics designed to improve learning of this difficult subject. Our simulations include several key features to help students build mental models and intuitions about quantum mechanics: visual representations of abstract concepts and microscopic processes that cannot be directly observed, interactive environments that directly couple students' actions to animations, connections to everyday life, and efficient calculations so students can focus on the concepts rather than the math. Like all PhET simulations, these are developed using the results of education research and feedback from educators, and are tested in student interviews and classroom studies. This article provides an overview of the PhET quantum simulations and their development. We also describe research demonstrating their effectiveness and share some insights about student thinking that we have gained from our research on quantum simulations.
I. INTRODUCTION
Quantum mechanics is difficult to learn because it is counterintuitive, difficult to visualize, mathematically challenging, and often disconnected from everyday life. PhET addresses these challenges with research-based interactive simulations, classroom testing, and an expanding suite of 18 quantum simulations.
- Quantum mechanics challenges students because microscopic phenomena are counterintuitive, difficult to observe directly, mathematically demanding, and abstracted from everyday experience.
- Research reports persistent learning difficulties across high school, undergraduate, junior-level, and graduate quantum mechanics courses.
- Prior research has concentrated on a few topics, leaving substantial need for tools and research addressing broader quantum concepts, applications, interpretations, and student beliefs.
- Educational simulations offer interaction, visualization, and context that may be especially helpful for developing intuition about abstract quantum principles.
- The paper overviews the simulations, their research-based development, classroom effectiveness studies, and insights into student thinking.
- 18 PhET quantum simulations span fundamental principles, historical experiments, and quantum principles underlying everyday applications.
A. Visualization
PhET simulations make unobservable quantum phenomena visible and connect students’ actions directly to animated representations. These features support mental-model construction and connections among representations.
- A. Visualization: Simulations visualize electrons, photons, atoms, wave interference, and other quantum phenomena that students cannot observe directly.
- A. Visualization: Photoelectric Effect lets students watch electrons move between plates and relate increased current to more electrons leaving the material.
- B. Interactivity: Interactive controls produce immediate animated responses, helping students engage with content and establish cause-and-effect relationships.
- B. Interactivity: Switching between representations helps students connect multiple representations of quantum phenomena.
- B. Interactivity: Quantum Bound States lets students change potential-well offset, height, and width and immediately observe effects on wave-function shape.
C. Context
PhET grounds quantum mechanics in familiar applications while using computer calculations and time-dependent animations to support qualitative exploration. These choices let instruction emphasize conceptual understanding and physically meaningful phenomena.
- C. Context: Simplified MRI connects nuclear spin and energy splitting to MRI, while Neon Lights connects atomic levels, energy transfer, photon emission, and spectra to discharge lamps.
- C. Context: Real-world applications help students relate quantum concepts to everyday experiences and appreciate the relevance of the physics.
- D. Taking advantage of the Computer: Computer calculations let students explore quantum tunneling and wave interference qualitatively without focusing on complex mathematical details.
- D. Taking advantage of the Computer: Quantum Tunneling and Wave Packets uses localized wave packets so students can visualize partial reflection and transmission at a barrier.
- D. Taking advantage of the Computer: Simulations allow students to observe atoms absorbing and emitting photons and wave functions changing over time.
III. DEVELOPING RESEARCH-BASED SIMS
PhET develops simulations through a research-based design cycle that combines learning goals, expert input, student interviews, and classroom use. The process evaluates clarity, accuracy, engagement, usability, and learning.
- The design cycle begins with content and interface experts creating a layout based on learning goals, education research, cognitive science, and PhET guidelines.
- Initial simulations are tested through student interviews to determine whether learners can use them and achieve the intended learning goals.
A. Building on Previous Research
PhET simulation design draws on learning research, content-specific research, and faculty-adoption research to support mental-model construction, reduce cognitive load, and address known student difficulties.
- Research-based design principles: Visualization, interactivity, familiar contexts, and removal of extraneous equipment details help students construct mental models and connect new concepts to prior knowledge.
- Research-based design principles: Simulations reduce cognitive load by beginning with simple states and progressively introducing more advanced features across tabs.
- Research-based design principles: PhET simulations are designed as open-ended, general-purpose tools so instructors can adapt them to local circumstances and learning goals.
- Addressing content-specific difficulties: Content research identified difficulties interpreting photoelectric-effect circuits, I-V graphs, intensity, wavelength, voltage, and the source of ejected electrons.
- Addressing content-specific difficulties: The Photoelectric Effect simulation addresses these difficulties with a physical circuit representation, interactive I-V graphs, and immediate responses to changes in intensity, wavelength, and voltage.
- Addressing content-specific difficulties: Because students often confuse wave functions with energy, two simulations display these quantities on separate graphs.
B. Observations of Students
Observations of students revealed conceptual gaps that existing instruction and simulations did not fully address, guiding the development of features and new simulations.
- Identifying student difficulties: Observations during lectures and problem-solving sessions were used to identify student difficulties and inform simulation design.
- Identifying student difficulties: Existing double-slit simulations showed screen patterns but did not help students visualize electron behavior between the slits and screen.
- Identifying student difficulties: Students studying Davisson-Germer often remembered angle-specific electron detections but did not understand their connection to electron wave behavior.
- Design response: Demonstrating wave-packet interference with an atom-like barrier array helped students explain the experiment, but manually changing the array was tedious.
- Design response: The Davisson Germer: Electron Diffraction simulation automated the atom array and enabled changes in spacing and size through a slider.
C. Student Interviews
Student interviews served both to refine simulation interfaces and to reveal how design choices affected conceptual understanding, interaction, and interpretation of scale.
- Interview-driven refinement: Students explored early simulation versions while thinking aloud, allowing developers to refine interfaces and pedagogical effectiveness.
- Interview-driven refinement: Replacing Photoelectric Effect’s separate simple and realistic models with a realistic default and an optional highest-energy-electrons filter shifted classroom questions toward the physics.
- Interview-driven refinement: The label ∆k led students to interpret it as “the change in k,” motivating attention to seemingly minor interface terminology.
- Interview-driven refinement: Students’ attempts to drag atom images rather than energy levels prompted Neon Lights and other Discharge Lamps to make both atoms and levels draggable.
- Persistent design limitations: Students did not clearly interpret visual cues for changing time and distance scales in Quantum Wave Interference, and the developers retained the cue as a reminder.
- Persistent design limitations: Combining atomic spectra and Rutherford scattering at an intermediate scale confused students about particle interactions, leading developers to separate Rutherford scattering into its own simulation.
A. Examples of Classroom Use
PhET quantum simulations were used as visual aids, interactive lecture demonstrations, and homework activities, prompting prediction, discussion, exploration, and deeper questions about quantum phenomena.
- Course uses: In a reformed large-lecture modern physics course, simulations supported visual aids, clicker-based prediction demonstrations, and guided homework exploration.
- Visual aids: Quantum Wave Interference illustrated that the double-slit experiment requires wave-like propagation through both slits and particle-like detection at one location.
- Visual aids: Students responded to this demonstration with questions about spatial spread, measurement, photon size, and how a wave-like object becomes localized.
- Visual aids: The visualization led students to ask foundational questions resembling those considered by the founders of quantum mechanics.
- Interactive lecture demonstrations: In an interactive tunneling lecture, students predicted with clickers, discussed answers, and compared the simulation’s partial reflection and transmission with the correct answer D.
- Interactive lecture demonstrations: After measurement, the tunneling simulation demonstrated that the electron is reflected or transmitted, rather than both simultaneously.
- Homework activities: Lasers homework guided students from absorption and emission through laser construction and troubleshooting, ending with essays about population inversion and three-level atoms.
B. Classroom testing of simulation effectiveness
Classroom studies found that PhET simulations supported learning across quantum-mechanics topics, although students also reported needing guidance and encountering occasional problems. In the Davisson–Germer study, performance improved substantially after simulation-supported instruction.
- Photoelectric Effect: 83% answered a photoelectric-effect exam question correctly with correct reasoning, compared with 20% in traditional instruction and 40% with a research-based tutorial.The question tested whether increasing plate voltage ejects electrons when light frequency is too low.
- Course-level outcomes: The reformed course produced high conceptual-learning gains and no shift in physics beliefs, unlike comparison courses with low gains and large negative belief shifts.The authors note that simulations played a large role among the course’s many reforms and likely contributed to these outcomes.
- Student perceptions: Students rated simulations 4.0 out of 5 for usefulness, while 80% of open-ended comments were positive.The survey included 173 students; other course aspects received ratings from 3.2 to 4.3.
- Student thinking: Qualitative observations found that students developed vivid mental models for topics taught with simulations.Students gave animated, rapid responses in interviews and problem-solving sessions about simulated topics.
- Davisson–Germer experiment: 35% of students admitted not doing or not remembering the assigned Davisson–Germer reading, complicating interpretation of the reading-quiz results.Quiz responses shown in Fig. 7b included only students who reported doing the reading.
- Davisson–Germer experiment: 92% of students correctly explained that the Davisson–Germer experiment revealed the wave nature of electrons on a midterm exam.The exam followed an interactive lecture using the simulation and homework requiring students to use it to explain the experiment.
V. LEARNING FROM STUDENT INTERVIEWS
Student interviews revealed both the concepts students could learn from PhET quantum simulations and the representations or conditions that impeded understanding. Interviews also guided revisions, identified misconceptions, and showed that guided activities often support learning beyond undirected exploration.
- Interview methods: Think-aloud interviews primarily identified simulation problems and informed design improvements, while also revealing student thinking and demonstrating effectiveness.Observations of students’ actions exposed interface needs that developers had not anticipated.
- Guidance and learning: Students often learned important concepts through exploration, but guided activities helped align exploration with instructional goals and broader context.The authors report measured learning gains with guided activities, although they did not directly compare guided and undirected exploration.
- Student understanding: Six students showed uneven understanding of quantum measurement: three explained wave-packet behavior independently, two after a hint, and one never did; all three tested in plane-wave mode were confused.The measurement button collapses the wave-packet probability density to a randomly positioned narrow packet, whereas plane-wave behavior required interviewer assistance to explain.
- Range of learners: Simulation suitability varied by preparation: several advanced simulations required prior knowledge, whereas others supported qualitative explanations from students without science or modern-physics backgrounds.Examples included Quantum Wave Interference, Lasers, Photoelectric Effect, Nuclear Physics, and Semiconductors for students without relevant backgrounds.
- Student understanding: Visual representations exposed incorrect prior models, including misconceptions about photon wave packets and the charge arrangement in the Plum Pudding model.These representations made student thinking visible in ways that could be difficult for instructors to detect otherwise.
- Representation choices: Most students could not interpret phase color: five of eight interviewed students either expressed frustration or offered unclear explanations, and none chose to spend much time in phase mode.The phase-color representation remained available for instructors but was accompanied by a recommendation for caution.
VI. CONCLUSION
PhET quantum simulations are designed around visualization, interactivity, context, and efficient computation to address students’ difficulties with abstract and counterintuitive quantum concepts. The research reported these simulations as effective in helping students understand quantum mechanics.
- Conclusion: PhET quantum simulations use visualization, interactivity, context, and effective computation to support understanding of abstract and counterintuitive quantum concepts.The simulations address previously known student difficulties and additional difficulties uncovered through research.