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We examine students’ challenges in determining the number of distinct many-particle stationary states for a system of noninteracting identical particles, focusing on how these insights guided the design, validation, and evaluation of a quantum interactive learning tutorial (QuILT) to aid students’ understanding. Specifically, we focus on systems with a fixed number of available single-particle states and particles, where the total energy is not fixed. The QuILT is designed to provide scaffolding support to help students learn these complex concepts more effectively. This study was conducted in advanced quantum mechanics courses, where written questions were administered to students in class following traditional instruction on the relevant concepts. Additionally, individual interviews were conducted with students to gain deeper insights. Our findings reveal that both upper-level undergraduate and graduate students face similar challenges in understanding these concepts. Additionally, difficulty with basic concepts in combinatorics that are necessary to answer the questions correctly was also found. The QuILT offers scaffolding support to help undergraduate and graduate students systematically reason through these concepts. Published by the American Physical Society2024
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This content will become publicly available on January 1, 2026
Teaching quantum formalism and postulates to first-year undergraduates
Traditional approaches to undergraduate-level quantum mechanics require extensive mathematical preparation, preventing most students from enrolling in a quantum mechanics course until the third year of a physics major. Here we describe an approach to teaching quantum formalism and postulates that can be used with first-year undergraduate students and even high school students. The only pre-requisite is a familiarity with vector dot products. This approach enables students to learn Dirac notation and core postulates of quantum mechanics at a much earlier stage in their academic career, which can help students prepare for careers in quantum science and engineering and advance the Second Quantum Revolution.
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- Award ID(s):
- 2309260
- PAR ID:
- 10597726
- Publisher / Repository:
- American Association of Physics Teachers
- Date Published:
- Journal Name:
- American Journal of Physics
- Volume:
- 93
- Issue:
- 1
- ISSN:
- 0002-9505
- Page Range / eLocation ID:
- 46 to 51
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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