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:

  1. They are based upon research in physics education and pay particular attention to cognitive issues.
  2. They employ visualization tools to help students build physical intuition about quantum processes.
  3. 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.
  4. 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.
  5. They are based on systematic investigations of difficulties students have in learning various concepts in quantum physics.
  6. 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.
  7. 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

Quantum Mechanics 2

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

Possible Wavefunction

Bound & Scattering States and Drawing Bound/Scattering states

Time Development

Dirac Notation QuILT and supplement

Mach Zehnder Interferometer QuILT and supplement

Double Slit Experiment QuILT and supplement

Quantum Key Distribution QuILT

Product Space QuILT

Identical Particles

Degenerate Perturbation Theory

Bloch Sphere

Basics of Quantum Computing

Packaged Quilts

Quantum Measurement

Stern Gerlach Experiment

Larmor Precession

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

Reflective Homework for second 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:
  • 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.