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[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] One hallmark of expertise in physics is the ability to translate between different representations of knowledge and use the representations that make the problem-solving process easier. In quantum mechanics, students learn about several ways to represent quantum states, e.g., as state vectors in Dirac notation and as wave functions in position and momentum representation. Many advanced students in upper-level undergraduate and graduate quantum mechanics courses have difficulty translating state vectors in Dirac notation to wave functions in the position or momentum representation and vice versa. They also struggle when translating the wave function between the position and momentum representations. The research presented here describes the difficulties that students have with these concepts and how the research was used as a guide in the development, validation, and evaluation of a Quantum Interactive Learning Tutorial (QuILT) to help students develop a functional understanding of these concepts. The QuILT strives to help students with different representations of quantum states as state vectors in Dirac notation and as wave functions in position and momentum representation and with translating between these representations. We discuss the effectiveness of the QuILT from in-class implementation and evaluation. Published by the American Physical Society2024
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This content will become publicly available on March 1, 2026
Improving student understanding of fermionic and bosonic wave function
[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] We discuss how research on student difficulties was used as a guide to develop, validate, and evaluate a Quantum Interactive Learning Tutorial (QuILT) to help students learn how to determine the completely symmetric bosonic or completely antisymmetric fermionic wave function and be able to compare and contrast them from the case when the particles can be treated as distinguishable. We discuss how explicit scaffolding is designed via guided teaching-learning sequences for two- or three-particle bosonic and fermionic systems to help students develop intuition about how to construct completely symmetric and antisymmetric wave function, both when spin part of the wave function is ignored and when both spatial and spin degrees of freedom are included. Published by the American Physical Society2025
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- Award ID(s):
- 2309260
- PAR ID:
- 10597738
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review Physics Education Research
- Volume:
- 21
- Issue:
- 1
- ISSN:
- 2469-9896
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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