Quantum Interactive Learning Tutorials (QuILTs)

Quantum Interactive Learning Tutorials (QuILTs)
Supporting physics teaching with research-based resources
About
Help
Contact
Expert Recommendations
Teaching
Assessment
Workshops
Curricula
»Quantum Interactive Learning Tutorials (QuILTs)
Quantum Interactive Learning Tutorials (QuILTs)
developed by Chandralekha Singh and PER team at the University of Pittsburgh
We are developing and assessing Quantum Interactive Learning Tutorials (QuILTs) for the advanced undergraduate courses. You can find more details on the
QuILTs page
on PhysPort. The following features of these materials make them particularly suited for the challenging task of teaching quantum physics:
They are based upon research in physics education and pay particular attention to cognitive issues.
They employ visualization tools to help students build physical intuition about quantum processes.
They consistently keep students actively engaged in the learning process by asking them to predict what should happen in a particular situation and then providing appropriate feedback.
They attempt to bridge the gap between the abstract quantitative formalism of quantum mechanics and the qualitative understanding necessary to explain and predict diverse physical phenomena without dumbing down the content.
They are based on systematic investigations of difficulties students have in learning various concepts in quantum physics.
The QuILTs can be used in class by the instructors once or twice a week as supplements to lectures or outside of the class as homework or as self-study tool by students.
The QuILTs consist of self-sufficient modular units that can be used in any order that is convenient.
Some QuILT modules expose students to contemporary and exciting topics such as quantum teleportation that can be taught using simple two-level systems.
The tutorial development goes through a cyclical iterative process that includes research on student difficulties in learning a particular physics concept, followed by the development, evaluation and refinement of the material. We are currently beta-testing several QuILT modules. If you are teaching quantum mechanics and would like to implement the modules in your class and provide us feedback, please send an email to
clsingh@pitt.edu
A majority of the computer-based visualization tools for this project are being developed by M. Belloni and W. Christian at Davidson College under the
Open Source Physics (OSP) Project
Concept Tests
The concept tests for quantum mechanics can be downloaded below. The order of the concept tests is based on the textbook of Griffiths. However, the concept tests are compatible with other QM textbooks.
Quantum Mechanics 1
Download the
Operators (Key)
Download the
Wavefunctions (Key)
Download the
Possible Wavefunction (Key)
Download the
Uncertainty Principle (Key)
Download the
Bound and Scattering States (Key)
Download the
Spin 1/2 - 1 (Key)
Download the
Spin 1/2 - 2 (Key)
Download the
Spin 1/2 - 3 (Key)
Download the
Stern-Gerlach (Key)
Download the
Coupled-Uncoupled Representations (Key)
Download the
Mach-Zehnder Interferometer (Key)
Download the
Mach-Zehnder Interferometer - Quantitative (Key)
Quantum Mechanics 2
Download the
Hydrogen Atom - 1 (Key)
Download the
Hydrogen Atom - 2 (Key)
Download the
Identical Particles - 1 (Key)
Download the
Identical Particles - 2 (Key)
Download the
Identical Particles - Atoms (Key)
Download the
Solids - 1 (Key)
Download the
Solids - 2 (Key)
Download the
Statistics - 1 (Key)
Download the
Statistics - 2 (Key)
Download the
Statistics - 3 (Key)
Download the
Perturbation Theory - 1 (Key)
Download the
Perturbation Theory - 2 (Key)
Download the
Perturbation Theory - 3 (Key)
Download the
Time Dependent Perturbation Theory - 1 (Key)
Download the
Time Dependent Perturbation Theory - 2 (Key)
Download the
Time Dependent Perturbation Theory - 3 (Key)
Download the
Selection Rules (Key)
Download the
Scattering Theory (Key)
Download the
Variational Method (Key)
Download the
WKB Approximation (Key)
Developed QuILTs
Here are the QuILTs we have developed so far. The simulation programs (.jar file) may need Java Runtime Environment (JRE) to run. (
Click here to download the JRE
) Some of the QuILTs have already be packaged in one jar file. For these packaged QuILTs, you can directly click the link in the jar file to release the documents (pdf files) such as pre/post tests or tutorials. Note that the pdf files will be released to the same folder as the jar file. So if you burn the jar file on a CD, the documents may not show up after you click the links in the file since there is no free space in the CD folder.
The
readme file (PDF)
contains the instructions on using QuILTs and the related references
Uncertainty Principle Part 1 and Part 2
Download the
0 - Heisenberg's Uncertainty Principle Readme (DOCX)
Download the
1 - Test A for Uncertainty I+II (DOC)
Download the
1 - Test B for Uncertainty I+II (DOC)
Download the
2 - Heisenberg's Uncertainty Principle (no answer) (DOC)
Download the
2 - Heisenberg's Uncertainty Principle (DOC)
Download the
3 - Heisenberg's Uncertainty Principle Part II (DOC)
Download the
3 - Heisenberg's Uncertainty Principle Part II (PDF)
Download the
Simulation Jar Files of Uncertainty Tutorials
Include "Free Particle Wave Packet", "Math Fourier Analysis" and "Multiple Slit Diffraction"
Possible Wavefunction
Download the
0 - Possible Wavefunction Readme (DOCX)
Download the
1 - Test A for Possible Wavefunction (DOC)
Download the
2 - Tutorial: Possible Wave Functions for Systems with a Single Particle Confined in One Spatial Dimension (DOC)
Download the
3 - Test B for Possible Wavefunction (DOC)
Download the
4 - Homework for Possible Wave functions for systems with a single particle confined in one spatial dimension (DOC)
Download the
Simulation Jar Files of Possible Wavefunction Tutorial
Include "bound-states_en", "ejs_qm_FreeParticleWavePacket" and "ejs_qm_Superposition"
Bound & Scattering States and Drawing Bound/Scattering states
Simulation of Quantum Bound State
Simulation of Quantum Tunneling and Wave Packet
Download the
0 - Bound & Scattering States Readme (DOCX)
Download the
1 - Test A for Bound & Scattering States (DOC)
Download the
2 - 1D Bound and Scattering States of a Single Particle Interacting with a Potential Energy (DOC)
Download the
3 - Test B for Bound & Scattering States (DOC)
Download the
4 - Solution to Material 2
Time Development
Download the
Time Tutorial
Dirac Notation QuILT and supplement
Download the
Dirac Notation QuILT Readme (DOCX)
Download the
Dirac Notation Quiz A (DOCX)
Download the
Post-Test: Dirac Notation Warm-Up (DOCX)
Download the
Dirac Notation Quiz B (DOCX)
Download the
Dirac Notation Warm-Up: Getting Acquainted with Dirac Notation in a Familiar Context (DOCX)
Download the
Dirac Notation Basics (DOCX)
Download the
Dirac Notation Homework (DOCX)
Mach Zehnder Interferometer QuILT and supplement
Download the
Mach Zehnder Interferometer QuILT Readme
Download the
Mach-Zehnder Interferometer (MZI) Warm-Up
Download the
Mach-Zehnder Interferometer (MZI): Pre-test
Download the
Mach-Zehnder Interferometer (MZI) with Single Photons: Tutorial
Download the
Mach-Zehnder Interferometer (MZI): Post-test
Download the
Understanding the Mach-Zehnder Interferometer (MZI) with Single Photons: Homework
Download the
Understanding the Mach-Zehnder Interferometer (MZI) with Single Photons: Hybrid version
Download the
Interferometer (ZIP)
Double Slit Experiment QuILT and supplement
Download the
0 - Double_Slit QuILT Readme (DOCX)
Download the
1 - Double-slit Experiment with Single Particles: Pretest (DOCX)
Download the
2 - Double-slit Experiment with Single Particles: Tutorial warm-up (DOCX)
Download the
3 - Double-slit Experiment with Single Particles: Tutorial (DOCX)
Download the
4 - Double-slit Experiment with Single Particles: Posttest (DOCX)
Download the
5 - Double-slit experiment with single electrons, "which-path" information and Dirac notation (DOCX)
Download the
5 - Double-slit experiment with single electrons, "which-path" information and Dirac notation (solution) (DOCX)
Download the
Double Slit Simulation (zip)
Quantum Key Distribution QuILT
Download the
0 - Quantum Key Distribution Readme (DOCX)
Download the
1 - Quantum Key Distribution Non-Orthogonal Polarization States Tutorial (PDF)
Download the
2 - Quantum Key Distribution Entanglement Tutorial PDF
Download the
3 - Quantum Key Distribution Entanlgement Pre-/Post-Test PDF
Product Space QuILT
Download the
0 - Product Space Readme (DOCX)
Download the
Combined File Product Space
Identical Particles
Download the
Identical Particles Tutorial
Download the
Identical Particles Pretest
Verification Required
Download the
Identical Particles Posttest
Verification Required
Degenerate Perturbation Theory
Download the
0 Basics of Degenerate Perturbation Theory Tutorial
Download the
1 Hydrogen Atom Warm-Up Tutorial
Download the
2 Hydrogen Atom Degenerate Perturbation Theory Tutorial
Download the
Degenerate Perturbation Theory Pretest
Verification Required
Download the
Degenerate Perturbation Theory Posttest
Verification Required
Bloch Sphere
Relevant reference: "Student understanding of the Bloch sphere", P. Hu, Y. Li, R. Mong and C. Singh Eur. J. Phys.  45, 025705 (2024)
Download the
Bloch Sphere Pre-test
Download the
Bloch Sphere Tutorial
Download the
Bloch Sphere Tutorial (Solutions)
Download the
Bloch Sphere Post-test
Download the
Bloch Sphere Post-test (Solutions)
Basics of Quantum Computing
Download the
Basics of Quantum Computing Pre-test
Download the
Basics of Quantum Computing Tutorial
Download the
Basics of Quantum Computing Tutorial (Solutions)
Download the
Basics of Quantum Computing Post-test
Download the
Basics of Quantum Computing Post-test (Solutions)
Download the
Basics of Quantum Computing 2nd Post-test (can be used on exams, etc.)
Packaged Quilts
Quantum Measurement
Download the
0 - Quantum Measurement QuILT Readme (DOCX)
Download the
1 - Test A for Measurement (PDF)
Download the
2 - Warm up for Quantum Measurement (no answer) (PDF)
Download the
2 - Warm up for Quantum Measurement (PDF)
Download the
3 - Quantum measurement without time evolution after measurement (no answer) (PDF)
Download the
3 - Quantum measurement without time evolution after measurement (PDF)
Download the
4 - Test B for Measurement (PDF)
Download the
Measurement Simulation
To load the simulation, please unzip the package and run the jar file
Stern Gerlach Experiment
Download the
0 - Stern-Gerlach Experiment QuILT Readme (DOCX)
Download the
1 - Test A for Stern-Gerlach Experiment (PDF)
Download the
2 - Warm-up for Stern-Gerlach & Larmor Precession Tutorials (PDF)
Download the
3 - Tutorial for Stern-Gerlach Experiment (PDF)
Download the
4 - Test B for Stern-Gerlach Experiment (PDF)
Download the
5 - Homework for Stern-Gerlach Experiment (PDF)
Download the
Stern Gerlach Experiment Simulation
Larmor Precession
Download the
0 - Larmor Precession QuILT Readme
Download the
1 - Test A for Larmor Precession (PDF)
Download the
2 - An electron in a uniform magnetic field: Larmor precession of spin (PDF)
Download the
3 - Test B for Larmor Precession (PDF)
Download the
Larmor Procession
To load the simulation, please unzip the package and run the jar file
Quantum Mechanics Survey
The Quantum Mechanics Survey is a 31-item multiple-choice test used to explore the conceptual difficulties that undergradutate and graduate students have with quantum mechanics.
Get the QMS Survey
Quantum Mechanics Formalism and Postulates Survey (QMFPS)
The Quantum Mechanics Formalism and Postulates Survey is a 34-item multiple-choice test used to explore student difficulties with the formalism and postulates of quantum mechanics.
Get the QMFPS Survey
Reflective Homework
The Reflective Homework is a set of open-ended questions helps students to review the contents learned in the undergraduate quantum mechanics course.
Reflective Homework for first semester
Here are the 14 reflective homework and solutions for the first semester QM course.  For some of the reflective homework (e.g., 1,2,3 and 5), there are different version marked with the suffix "last" or "last_new".
Download the
Reflective Homework for 1st semester
Reflective Homework for second semester
Here are the 4 reflective homework and solutions for the second semester QM course.
Download the
Reflective Homework for 2nd semester
Clicker Question Sequences (CQS)
These are folders for several of our clicker question sequences (CQS) for quantum mechanics.  Many of these CQSs were developed taking instructional inspiration from research done in the development of analogous quantum interactive learning tutorials (QuILTs), and therefore have with them the same validated pre/posttest and solutions.  Others of these CQSs were developed in the spirit of such instruction, but required quizzes to be written separately.
Download the
Addition of Angular Momentum
Download the
Bound Scattering States
Download the
Degenerate_Perturbation_Theory
Download the
Dirac_Notation
Download the
Free Electron Gas Model
Download the
Hydrogen_Atom
Download the
Identical_Particles
Download the
Larmor_Precession
Download the
Possible_Wavefunction
Download the
Quantum_Key_Distribution (QKD)
Download the
Quantum_Measurement
The CQS of Quantum_Measurement is updated in Feb 2025
Download the
Stern-Gerlach_Experiment
Download the
Time Development of Wave Function
Download the
Time_Dependent_Perturbation_Theory
Download the
Uncertainty_Principle
Download the
Change of Basis (Two-state systems)
Relevant reference:  "Challenges in addressing student difficulties with basics and change of basis for two-state quantum systems using a multiple-choice question sequence in online and in-person classes" P. Hu, Y. Li and C. Singh, Eur. J. Phys. 44, 065703 (2023). http://doi.org/10.1088/1361-6404/acf5b3
Download the
Time Development (Two-state systems)
Revelant reference: "Challenges in addressing student difficulties with time-development of two-state quantum systems using a multiple-choice question sequence in virtual and in-person classes", P. Hu, Y. Li and C. Singh, Eur. J. Phys. 43, 025704 (2022). https://doi.org/10.1088/1361-6404/ac49f4
Download the
Quantum Measurement (Two-state systems)
Relevant reference: "Challenges in addressing student difficulties with quantum measurement of two-state quantum systems using a multiple-choice question sequence in online and in-person classes", P. Hu, Y. Li and C. Singh, Physical Review Physics Education Research 19 (1), 020130 (2023). https://doi.org/10.1103/PhysRevPhysEducRes.19.020130
Download the
Measurement Uncertainty (Two-state systems)
Relevant reference: "Challenges in addressing student difficulties with measurement uncertainty of two-state quantum systems using a multiple-choice question sequence in online and in-person classes", P. Hu, Y. Li and C. Singh, Eur. J. Phys. 44, 015702 (2022). https://doi.org/10.1088/1361-6404/ac9ba3
* QuILT is supported by the National Science Foundation.
** Some simulations used in QuILT are adapted from opensourcephysics.org and PhET.
We are grateful to Dr. Wolfgang and Dr. Belloni for helping us integrating the opensourcephysics simulations into QuILT.
We also thank PhET team for the helpful interactive simulations in quantum mechanics.
Feedback
Expert Recommendations
Teaching Methods
Assessment
Workshops
Data Explorer
About
Help
Contact
My Account
Contact PhysPort
brought to you by the
AAPT
funded by the
NSF