Exploring Student Ideas on Change of Basis in Quantum Mechanics

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...

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Bibliographic Details
Published inPhysical Review Physics Education Research Vol. 18; no. 1; pp. 010144 - 10157
Main Authors Corsiglia, Giaco, Schermerhorn, Benjamin P, Sadaghiani, Homeyra, Villaseñor, Armando, Pollock, Steven, Passante, Gina
Format Journal Article
LanguageEnglish
Published College Park American Physical Society 01.06.2022
Subjects
Change
Concept Formation
Physics
Problem Solving
Quantum Mechanics
Quantum physics
Science Instruction
Scientific Concepts
State vectors
Student Attitudes
Students
Teaching Methods
Thermal expansion
Thinking Skills
Undergraduate Students
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Summary: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-½ 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.
ISSN:2469-9896
2469-9896
DOI:10.1103/PhysRevPhysEducRes.18.010144