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 student 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. A comparison with the base line data on the validated QMFPS presented here can aid instructors in assessing the effectiveness of their instructional approaches.

References in corpus (6)

• Development and validation of a sequence of clicker questions for helping students learn addition of angular momentum in quantum mechanics
• Quantum interactive learning tutorial on the double-slit experiment to improve student understanding of quantum physics
• Student understanding of Fermi energy, the Fermi-Dirac distribution and total electronic energy of a free electron gas
• Effectiveness of interactive tutorials in promoting "which-path" information reasoning in advanced quantum mechanics
• Developing and evaluating an interactive tutorial on degenerate perturbation theory
• Development, validation and in-class evaluation of a sequence of clicker questions on Larmor precession of spin in quantum mechanics

Cited by in corpus (13)

• Introductory quantum information science coursework at US institutions: Content coverage
• Student understanding of Fermi energy, the Fermi-Dirac distribution and total electronic energy of a free electron gas
• Multilingual Performance of a Multimodal Artificial Intelligence System on Multisubject Physics Concept Inventories
• Student Understanding of the Bloch Sphere
• Can students apply the concept of "which-path" information learned in the context of Mach Zehnder Interferometer to the double-slit experiment?
• Peer interaction facilitates co-construction of knowledge in quantum mechanics
• 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
• 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
• 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
• Using multiple representations to improve student understanding of quantum states
• Insights from Educators on Building a More Cohesive Quantum Information Science and Engineering Education Ecosystem
• Improving student understanding of quantum measurement in infinite-dimensional Hilbert space using a research-based multiple-choice question sequence
• Do we have a quantum computer? Expert perspectives on current status and future prospects