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.
Highlights
Learning quantum mechanics (QM) is challenging partly because it is abstract as well as nonintuitive and students often transfer ideas from classical mechanics to quantum mechanics inappropriately [1,2,3,4]
To ensure that the survey is valid for low-stakes group assessment of QM curriculum and instructional approaches that focus on relevant topics, we consulted with 6 faculty members regarding the goals of their QM courses and topics their students should have learned related to the formalism and postulates of quantum mechanics in upper-level undergraduate QM
Learning QM is challenging for students partly because of the “paradigm shift” from classical mechanics to quantum mechanics as well as the mathematical expertise required to solve problems
Summary
Learning quantum mechanics (QM) is challenging partly because it is abstract as well as nonintuitive and students often transfer ideas from classical mechanics to quantum mechanics inappropriately [1,2,3,4]. The quantum mechanics conceptual survey (QMCS) [31] was developed for sophomore-level modern physics courses It focuses on wave functions and probability, wave particle duality, the Schrodinger equation, quantization of states, uncertainty principle, superposition, operators and observables, and tunneling. The quantum mechanics survey (QMS) [36] covers topics in nonrelativistic quantum mechanics in one spatial dimension typically covered in the first semester of an upper-level undergraduate course and involves concepts such as possible wave functions, bound or scattering states, measurement, expectation values, time dependence of wave function and expectation values, stationary and nonstationary states, role of the Hamiltonian, uncertainty principle, and Ehrenfest’s theorem. The survey can be used to identify upper-level undergraduate students’ final and graduate students’ initial and final knowledge states related to the formalism and postulates of quantum mechanics at the beginning and end of a course to assess the effectiveness of a quantum mechanics curriculum in which relevant concepts are covered. The results of the survey can be used to guide the development of instructional strategies to help students learn these concepts better
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