Exploring student ideas on change of basis in quantum mechanics
Open Access
- 6 June 2022
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Physics Education Research
- Vol. 18 (1), 010144
- https://doi.org/10.1103/physrevphyseducres.18.010144
Abstract
A common task when problem solving in quantum mechanics, including in a spins-first curriculum, involves changing the basis of a given state. Our research in undergraduate quantum mechanics courses at three institutions explores student thinking about basis, basis expansion coefficients, and change of basis in the context of spin- systems. Our investigation is based on conceptual and computational written questions as well as student reasoning interviews. We identify student ideas about whether and how changing basis affects the state, examine how students perceive notation as indicative of choice of basis, explore students’ interpretations of the structure and meaning of a basis expansion, and identify the range of methods students employ when changing basis. For instance, we find a recurring idea that changing basis alters the physical system, and observe that some students chose to relabel the ket representing a quantum state vector after changing basis. Together, these results paint a broad, qualitative picture of a variety of ways that students grapple with basis and change of basis, with potential implications for instruction.
Keywords
Funding Information
- National Science Foundation (DUE 1626280, 1626594, 1626482)
This publication has 29 references indexed in Scilit:
- Review of student difficulties in upper-level quantum mechanicsPhysical Review Special Topics - Physics Education Research, 2015
- Analyzing student understanding in linear algebra through mathematical activityThe Journal of Mathematical Behavior, 2015
- Emphasizing language and visualization in teaching linear algebraInternational Journal of Mathematical Education in Science and Technology, 2013
- Improving students’ understanding of quantum measurement. I. Investigation of difficultiesPhysical Review Special Topics - Physics Education Research, 2012
- Representations for a spins-first approach to quantum mechanicsAIP Conference Proceedings, 2012
- Student learning of basis, span and linear independence in linear algebraInternational Journal of Mathematical Education in Science and Technology, 2010
- Student understanding of quantum mechanics at the beginning of graduate instructionAmerican Journal of Physics, 2008
- Difficulties in learning the introductory magnetic field theory in the first years of universityScience Education, 2004
- Student resources for learning introductory physicsAmerican Journal of Physics, 2000
- Phenomenography ? Describing conceptions of the world around usInstructional Science, 1981