Validation and administration of a conceptual survey on the formalism and postulates of quantum mechanics

Abstract

We developed and validated a conceptual survey that focuses on the formalism and postulates of quantum mechanics covered in upper-level undergraduate quantum mechanics courses. The concepts included in the Quantum Mechanics Formalism and Postulate Survey (QMFPS) focus on Dirac notation, the Hilbert space, state vectors, physical observables and their corresponding Hermitian operators, compatible and incompatible observables, quantum measurement, time-dependence of quantum states and expectation values, and spin angular momenta. Here we describe the validation and administration of the survey, which has been administered to over 400 upper-level undergraduate and graduate students from six institutions. The QMFPS is valid and reliable for use as a low-stakes test to measure the effectiveness of instruction in an undergraduate quantum mechanics course that covers relevant content. The survey can also be used by instructors to identify students' understanding of the formalism and postulates of quantum mechanics at the beginning and end of a graduate quantum mechanics course since graduate students are expected to have taken an undergraduate quantum mechanics course that covers the content included in the survey. We found that undergraduate students who engaged with research-validated learning tools performed better than students who did not on the QMFPS after the first semester of a junior/senior level quantum mechanics course. In addition, the performance of graduate students on QMFPS after instruction in the first semester of a core graduate-level quantum mechanics course was significantly better than the performance of undergraduate students at the end of the first semester of an undergraduate quantum mechanics course. However, both undergraduate and graduate students struggled with many questions on the QMFPS. A comparison with the base line data on the validated QMFPS presented here can aid instructors in assessing the effectiveness of their instructional approaches and help them identify the difficulties their students have with quantum formalism and postulates in order to help students develop a solid grasp of the formalism and postulates of quantum mechanics. I.

Effectiveness of guided group work in graduate level quantum mechanics

“…In that same study, the number who drew an excited state correctly was significantly lower: 7% on the pretest and 5% on the post-test. Similar studies exist for graduate student understanding of quantum mechanical spin [17,18] and hydrogen [19].…”

Peer interaction facilitates co-construction of knowledge related to quantum mechanics formalism and postulates

“…The QMFPS is a validated survey which includes topics that were not focused on in other QM surveys [19], such as Dirac notation, Hilbert space, state vectors, physical observables and their corresponding Hermitian operators, compatible and incompatible observables, projection operators and writing operators in terms of their eigenstates and eigenvalues, and spin angular momentum. The final version of the survey contains 34 multiple-choice items and is designed primarily for junior/senior-level undergraduates and first-year graduate students.…”

“…The final version of the survey contains 34 multiple-choice items and is designed primarily for junior/senior-level undergraduates and first-year graduate students. It has been validated [19] using initial faculty and student interviews, learning from previous open-ended and multiple-choice questions given to QM students, and additional faculty and student interviews for each iteration of the survey. Student interviews served multiple purposes, including assuring that students interpreted questions as intended and development of alternative incorrect choices for multiple-choice questions aligned with common student difficulties when the questions were presented as open-ended questions [19].…”

“…It is not clear a priori how much students will benefit from unguided peer discussions during their collaboration particularly because the paradigm of QM differs from introductory physics and has the potential to affect peer interaction. However, even though QM is abstract and nonintuitive, students often have common difficulties in learning this new paradigm and research shows that they sometimes transfer ideas from classical to quantum contexts or from one quantum context to another quantum context in which those ideas are not applicable [19]. In other words, even in the QM contexts, students' reasonings in different contexts show patterns, which can impact the manner in which students are likely to construct and co-construct knowledge during unguided peer collaboration.…”

Development, validation and online and in-person implementation of clicker question sequence on quantum measurement uncertainty

“…Prior research suggests that students in QM courses often struggle with many common difficulties [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. However, research-validated learning tools can help students develop a robust knowledge structure [19][20][21][22][23][24][25]. For example, our group has developed, validated and implemented Quantum Interactive Learning Tutorials (QuILTs) with encouraging results on many topics in QM [1,[26][27][28][29][30][31][32].…”