Quantum Mechanics Concept Assessment (QMCA)

Developed by Homeyra Sadaghiani and Steven Pollock

Purpose To assess students’ knowledge about main topics of quantum measurement at the junior level.
Format Multiple-choice
Duration 50 min
Focus Modern / Quantum Content knowledge (wave functions, measurement, time dependence, probability, infinite square well, 1D tunneling, energy levels, spins)
Level Upper-level
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Sample questions from the QMCA:

QMCA Implementation and Troubleshooting Guide

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H. Sadaghiani and S. Pollock, Quantum mechanics concept assessment: Development and validation study, Phys. Rev. ST Phys. Educ. Res. 11 (1), 010110 (2014).
External Resources

The Colorado Science Education Initiative (SEI) and collaborators have developed a wide range of curricular materials for teaching junior-level quantum mechanics, of which the QMCA is only one. Other materials include group activities, clicker questions, and homework.

The SEI QM I page has materials for teaching quantum mechanics using a wave functions first approach.

The Adaptable Curricular Exercises for Quantum Mechanics page has materials for teaching quantum mechanics using a spins first approach.

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Silver Validation
This is the second highest level of research validation, corresponding to at least 5 of the validation categories below.

Research Validation Summary

Based on Research Into:

  • Student thinking

Studied Using:

  • Student interviews
  • Expert review
  • Appropriate statistical analysis

Research Conducted:

  • At multiple institutions
  • By multiple research groups
  • Peer-reviewed publication

The multiple-choice questions on the QMCA were developed by first converting the open-ended questions on the QMAT to a multiple-choice format and creating eight new questions. To create the multiple-choice answers, open-ended responses to QMAT questions, responses in student interviews, and expert feedback were used and a literature review was conducted. This initial version of the QMCA was given to over 50 students, and 13 of these students participated in follow-up interviews. The questions were revised and given to an additional 263 students taking upper-division quantum mechanics at 10 intuitions. Appropriate statistical analysis of reliability, difficulty and discrimination were conducted and reasonable values were found. The QMCA has been tested with over 300 students and the results are published in two peer-reviewed publications.


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Language Translator(s)  
Portuguese Ricardo Kagimura

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Typical Results

Typical scores on the QMCA Version 5.5.7 from Sadaghiani and Pollock 2014. Below are students’ mean scores on the beta version of QMCA, organized based on the type of university. (Repeated name codes mean consecutive semesters at the same institution) N is the number of students in the class. The red dashed line represents the weighted average for all students across different institute, which was 54%.

The latest version of the QMCA, released in Fall 2018, is version 6.6.2. Version 6.6.2 contains BOTH spins and wave functions variants of some questions. The previous version, Version 5.5.7, included only questions with a wave function context (no spin). This instrument was adapted from an open-ended instrument known as the Quantum Mechanics Assessment Tool (QMAT). Earlier versions of the multiple-choice version were known as the QMAT-MC, before it was renamed the QMCA.