Which quantum mechanics or modern physics researchbased assessment should I use in my class?
This recommendation initially appeared as an article in the American Journal of Physics: A. Madsen, S. B. McKagan and E. C. Sayre, Resource Letter RBAI1: ResearchBased Assessment Instruments in Physics and Astronomy, Am. J. Phys. 85, 4 (2017).
There are seven tests covering modern physics and/or quantum mechanics content for sophomore, junior, senior, and graduate level courses. These tests were developed starting in the early 2000s and until very recently. All cover a broad range of topics. These tests are discussed below in groups based on the level of course they are appropriate for. There are two additional graduate quantum mechanics surveys, but these are not researchbased and validated, so they will not be discussed further below (Carr and McKagan 2008; Singh 2008). Intermediatelevel tests, such as for Modern Physics courses, are summarized in Table 1; assessments for upperlevel and graduate courses are in Table 2.
Table 1. Modern physics assessments.
Title  Content  Intended Population  Research Validation  Purpose 
Relativity 

Special relativity 
Intro college  Silver 
Measure changes in students’ conceptual understanding of special relativity and identify students’ misconceptions. 

Intermediate quantum mechanics 

Quantum Physics Conceptual Survey (QPCS) 
Photoelectric effect, wave particle duality, de Broglie wavelength, double slit interference, uncertainty principle 
Intro college, intermediate 
Silver 
Investigate students’ understanding of introductory quantum physics concepts. 
Quantum Mechanics Conceptual Survey (QMCS) 
Wave functions, probability, infinite square well, onedimensional tunneling, waveparticle duality, energy levels, uncertainty principle 
Intermediate 
Silver 
Measure the effectiveness of different teaching methods at improving students’ conceptual understanding of quantum mechanics, and to use such measurements to improve their teaching. 
Quantum Mechanics Concept Inventory (QMCI) 
Wave functions, probability, 1D tunnelling 
Intermediate, upperlevel 
Researchbased 
Assess students’ alternative conceptions around 1D potential barriers, tunneling, and probability distributions. 
Relativity assessment
Relativity Concept Inventory (RCI)
The Relativity Concept Inventory (RCI) (Aslanides and Savage 2013) is the only RBAI that covers special relativity and is for introductory undergraduate courses that cover relevant relativity topics. This is a pre/post conceptual multiplechoice assessment where students are asked to also rate their confidence for each question. Topics covered include time dilation, length contraction, relativity of simultaneity, inertial reference frames, velocity addition, causality, and massenergy equivalence. The questions were developed based on a list of concepts informed by the learning goals for a relevant course, textbooks, and the research literature. Use the RCI if you want to assess your students’ conceptual understanding of special relativity and the effectiveness of your instruction.
Intermediate quantum mechanics assessments
There are three tests designed for sophomorelevel quantum mechanics: the Quantum Physics Conceptual Survey (QPCS) (Larkin, Meade, and Uscinski 2011; Wuttiprom et al. 2009) the Quantum Mechanics Conceptual Survey (QMCS) (McKagan, Perkins, and Wieman 2010), and the Quantum Mechanics Concept Inventory (QMCI) (Falk 2004). There is one additional quantum assessment, the Quantum Mechanics Visualization Instrument (QMVI), which can be used at multiple levels, including intermediate, upperlevel, and graduate quantum, so it will be discussed in the “Upperlevel quantum mechanics assessment and beyond” section below.
Quantum Physics Conceptual Survey (QPCS)
The Quantum Physics Conceptual Survey (QPCS) (Larkin, Meade, and Uscinski 2011; Wuttiprom et al. 2009) is a pre/post conceptual assessment that can be used at the introductory level (if you have covered these topics) and in a sophomorelevel modern physics course. There are no equations on the QPCS and most questions focus on waveparticle duality and the photoelectric effect (this is the only quantum test which includes the photoelectric effect). Most of the questions are structured in a way that asks the students about what happens when they do a specific experiment. The multiplechoice questions on the QPCS were developed based on topics common across several introductory quantum syllabi, expert opinion, and student ideas that emerged through openended questions. It was developed in Thailand and tested in Thailand and Australia.
Quantum Mechanics Conceptual Survey (QMCS)
The Quantum Mechanics Conceptual Survey (QMCS) (McKagan, Perkins, and Wieman 2010) is a highly conceptual multiplechoice assessment for sophomorelevel students. The QMCS can be given as a posttest only at the end of the term in a sophomorelevel modern physics course. It can be given as both a pre and posttest to measure student learning in a juniorlevel course or higher. Some of the questions on the QMCS probe ideas that students have about quantum mechanics, as uncovered in student interviews. For example, one question asks about electrons moving in sinusoidal paths, because interviews found that this is how many undergraduates think about the motion of an electron. The QMCS does not explicitly include equations, but it does ask students to think about qualitative relationships in equations. The questions on the QMCS were developed based on faculty interviews, a review of textbooks and syllabi, observations of students, and a literature review of known student difficulties. A few of the questions on the QMCS come from other tests (questions 10 and 11 are from the QMVI). Further, the QMCS covers many quantum mechanics topics, but only has 12 questions, so is limited in what it can tell you about what your students learned.
Quantum Mechanics Concept Inventory (QMCI)
The Quantum Mechanics Concept Inventory (QMCI) (Falk 2004) is a pre/post multiplechoice assessment which is very conceptual in nature with no equations included and simple language. The question format gives statements from a hypothetical student about a given concept and your students have to pick which one they agree with. It was designed to diagnose students’ alternative conceptions about quantum mechanics, so each answer choice is associated with a specific alternative conception. It is meant for sophomore and juniorlevel students. Questions are based on students’ ideas about quantum as documented in the literature. The QMCI was developed in Sweden.
Unlike the QMCS, the questions on the QMCI are about a narrow range of topics, with most questions asking about tunneling through onedimensional barriers. Similar to the QMCS, the QMCI is very conceptual in nature and only has a few questions (nine for the QMCI), so it is limited in what it tells you about what your students learned.
Recommendations for choosing an intermediate quantum mechanics assessment
If you are teaching a sophomorelevel modern physics course, use the QMCS if you want a broad overview of course topics and the QMCI if you want an indepth test of onedimensional potential barriers, tunneling, and probability distribution. Use the QPCS if you want to test photoelectric effect or a more indepth treatment of wave particle duality. Use QMVI if you want a very detailed look at the relationship between the wave function and shape of potential. The QMVI contains questions from several levels of quantum mechanics, so expect your sophomorelevel students to do poorly on most questions.
Upperlevel quantum mechanics assessments and beyond
There are four tests that are designed to assess students’ understanding of quantum at the junior level: The Quantum Mechanics Concept Assessment (Sadaghiani et al. 2013; Sadaghiani and Pollock 2014) (QMCA), the Quantum Mechanics Assessment Tool (QMAT) (Goldhaber et al. 2009), the Quantum Mechanics Survey (QMS) (Zhu and Singh 2012), and the Quantum Mechanics Formalism and Postulates Survey (QMFPS) (Marshman 2015). The Quantum Mechanics Visualization Instrument (QMVI) (Robinett and Cataloglu 2002) can be used at several levels and will also be discussed in this section.
Table 2. Upperlevel quantum mechanics assessments.
Title  Content  Intended Population  Research Validation  Purpose 
Upperlevel quantum mechanics 

Wave functions, probability, infinite square well, 1D tunneling, energy levels, measurement, time dependence 
Upperlevel 
Silver 
Assess students’ knowledge about main topics of quantum measurement at the junior level. Also compare outcomes of different curricular approaches. 

Quantum Mechanics Survey (QMS) 
Wave functions, probability, infinite square well, 1D tunneling, energy levels, measurement, time dependence 
Upperlevel and graduate 
Silver 
Assess students’ conceptual understanding of quantum mechanics, specifically their proficiency with the formalism of quantum mechanics in 1D. 
Formalism and postulates of quantum mechanics 
Upperlevel and graduate 
Silver 
Assess students’ conceptual understanding of the formalism and postulates of quantum mechanics rather than their mathematical skills. 

Wave functions, probability, infinite square well, 1D tunneling, time dependence, momentum space, 2D potentials, visualization of the relationship between potentials and wave functions 
Intermediate, upperlevel and graduate 
Silver 
Probe the development of students’ conceptual understanding of core topics in quantum mechanics across the undergraduate curriculum, especially their visualization skills. 

Quantum Mechanics Assessment Tool (QMAT) 
Wave functions, probability, infinite square well, 1D tunneling, energy levels, measurement, time dependence 
Upperlevel 
Bronze 
Measure student learning of the quantum mechanics concepts most valued by faculty, assess student learning difficulties, and inform course improvement 
Quantum Mechanics Concept Assessment (QMCA)
The Quantum Mechanics Concept Assessment (QMCA) (Sadaghiani et al. 2013; Sadaghiani and Pollock 2014) is one of the newer quantum mechanics assessments for a firstsemester juniorlevel quantum mechanics course. It assesses students’ understanding of five main topics of quantum measurement: the timeindependent Schrödinger equation, wave functions, boundary conditions, time evolution, and probability density. The QMCA includes math formalism, but most of the questions rely on qualitative understanding of the relationships between equations rather than quantitative calculations. It contains many questions about the Schrödinger equation and a few about measurement as a theoretical construct (e.g., given a wave function, make a measurement, what is the new wave function). There are many questions that use infinite square well potentials and a couple which ask students to think about nonstandard potentials qualitatively. The developers recommend using the QMCA as a posttest for sophomore level modern physics classes. It could be used as a pretest in graduate level quantum to see if students have sufficient conceptual understanding of undergraduate level quantum topics. The multiplechoice questions on the QMCA were developed using the openended questions on the QMAT as a starting point.
Quantum Mechanics Assessment Tool (QMAT)
The Quantum Mechanics Assessment Tool (QMAT) (Goldhaber et al. 2009) questions are openended and are a mix of conceptual and math intensive questions, where students are asked to solve equations in some of the questions. The QMAT covers the same five main topics of quantum measurement as the QMCA and is also meant for a firstsemester juniorlevel quantum mechanics. It should be given as a posttest only at the end of the term. It was designed to measure student learning of concepts most valued by faculty, assess students’ learning difficulties, and inform course improvement. The content of the QMAT is based on working with faculty to determine learning goals for quantum mechanics. A couple of the questions were taken from an early version of the QMCS. There is a rubric for grading the test, but the rubric requires extensive training to get acceptable interrater reliability. Further, because this is an openended assessment it is difficult to compare results to other institutions. There are limited validation studies of the QMAT, and it has been archived by the developers, so you should use the QMCA, unless you specifically want a shortanswer test. Further, the QMCA has been more thoroughly researched and validated.
Quantum Mechanics Survey (QMS)
The Quantum Mechanics Survey (QMS) (Zhu and Singh 2012) is a multiplechoice assessment for the junior and graduatelevel. The QMS has a wide range of topics including wave functions, the expectation value of a physical observable and its time dependence, the role of the Hamiltonian, stationary and nonstationary states and issues related to their time development, and measurements.66 All questions are restricted to onedimensional quantum mechanics models. The QMS should be given as a posttest only in a juniorlevel course, but can be given as a pre and posttest in a graduate level quantum course. The QMS was designed not only to assess students’ conceptual understanding of quantum mechanics but also contains an extensive mathematical formalism. Although students do not have to complete difficult integrals to solve any of the questions, they do need to understand the basics of linear algebra. Topics covered on the QMS are those that faculty find important for juniorlevel quantum mechanics courses.
The content covered by the QMS and QMCA is very similar, but the QMS is more difficult and mathematical than the QMCA, and contains a lot more equations. Both have similar formats and levels of research validation.
Quantum Mechanics Formalism and Postulates Survey (QMFPS)
The Quantum Mechanics Formalism and Postulates Survey (QMFPS) (Marshman 2015) is the newest quantum mechanics assessment. It assesses students’ understanding of the formalism and postulates of quantum mechanics. The QMFPS is a pre/ post multiplechoice test that is appropriate for junior/senior level quantum mechanics courses where Dirac notation has been covered similar to coverage in the first four chapters of Griffiths. The QMFPS is not meant to assess students’ mathematical skills, but students do need to know the basics of linear algebra to answer the questions. The multiplechoice questions on the QMFPS were developed based on expert feedback about relevant topics, review of course materials, and a subsequent test blueprint. The QMFPS, like the QMCA and the QMS, is meant to assess students’ conceptual understanding of quantum mechanics, but the QMFPS focuses particularly on students’ understanding of the formalism and postulates of quantum mechanics.
Quantum Mechanics Visualization Instrument (QMVI)
The Quantum Mechanics Visualization Instrument (QMVI) (Robinett and Cataloglu 2002) is a multiplechoice exam and was the first quantum mechanics survey created. It was designed to assess students’ understanding of quantum topics at all levels, from sophomorelevel to graduatelevel. Most of the questions are about the relationship between the shape of the potential and the wave function, with an emphasis on visualizing this relationship. There are a few questions about the uncertainty principle, and two questions about momentum space probability distributions. Some of the questions require “tricks” to figure out, e.g., making a symmetry argument makes a question very easy, but without the symmetry argument, it is very difficult. The questions are multiplechoice, and also ask students to give a 2–3 line written response and a rating of their confidence level. The QMVI contains 25 questions at all different levels, with very simple questions for sophomorelevel students, and very difficult questions for graduatelevel students. Because of the variety in difficulty of the questions, it can be used to track students’ progress throughout the quantum course sequence. Since it contains questions at the graduatelevel, it is a very difficult test. The QMVI contains extensive mathematical formalism. The developers recommend giving it as an extended takehome exam, as it can take up to two hours for students to complete. The topics covered are those that authors feel are important for students to learn in the quantum sequence.
Recommendations for choosing an upperlevel quantum mechanics assessment
If you are teaching a junior or seniorlevel quantum mechanics course, which test you use depends on both the difficulty level and the range of topics you want to cover: In terms of difficulty, the QMCS is at the lowest level, followed by the QMCI and QPCS, the QMCA, and then the QMVI, QMFPS, and QMS. In terms of content, all quantum RBAIs cover some basic ideas about wave functions. The QMVI focuses in great depth on the relationship between the wave function and the shape of the potential. The QPCS is the only assessment that covers the photoelectric effect. The QMCI is entirely conceptual, whereas the QMCA, QMFPS, and QMS require some formalism. The QMFPS has a different focus than the other upperlevel quantum assessments, and should be used if you want to specifically assess your students’ understanding of quantum formalism and postulates.
References
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 L. Carr and S. McKagan, Graduate Quantum Mechanics Reform, Am. J. Phys. 77 (4), 308 (2008).
 J. Falk, Developing a quantum mechanics concept inventory, Masters, Uppsala University, 2004.
 S. Goldhaber, S. Pollock, M. Dubson, P. Beale, and K. Perkins, Transforming UpperDivision Quantum Mechanics: Learning Goals and Assessment, presented at the Physics Education Research Conference 2009, Ann Arbor, Michigan, 2009.
 T. Larkin, P. Meade, and J. Uscinski, Probing a deeper understanding of modern physics concepts, presented at the Frontiers in Education Conference, Rapid City, SD, 2011.
 E. Marshman, Improving the Quantum Mechanics Content Knowledge and Pedagogical Content Knowledge of Physics Graduate Students, University of Pittsburgh, 2015.
 S. McKagan, K. Perkins, and C. Wieman, Design and validation of the Quantum Mechanics Conceptual Survey, Phys. Rev. ST Phys. Educ. Res. 6 (2), 020121 (2010).
 R. Robinett and E. Cataloglu, Testing the development of student conceptual and visualization understanding in quantum mechanics through the undergraduate career, Am. J. Phys. 70 (3), 238 (2002).
 H. Sadaghiani, J. Miller, S. Pollock, and D. Rehn, Constructing a Multiplechoice Assessment for Upperdivision Quantum Physics from an Openended Tool, presented at the Physics Education Research Conference 2013, Portland, OR, 2013.
 H. Sadaghiani and S. Pollock, Quantum mechanics concept assessment: Development and validation study, Phys. Rev. ST Phys. Educ. Res. 11 (1), 010110 (2014).
 C. Singh, Student understanding of quantum mechanics at the beginning of graduate instruction, Am. J. Phys. 76 (3), 277 (2008).
 S. Wuttiprom, M. Sharma, I. Johnston, R. Chitaree, and C. Soankwan, Development and Use of a Conceptual Survey in Introductory Quantum Physics, Int. J. Sci. Educ. 31 (5), 631 (2009).
 G. Zhu and C. Singh, Surveying students' understanding of quantum mechanics in one spatial dimension, Am. J. Phys. 80 (3), 252 (2012).