An official website of the United States government
[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
more »
« less
This content will become publicly available on December 1, 2025
Improving student understanding of the number of distinct many-particle states for a system of identical particles with a fixed number of available single-particle states
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
more »
« less
- Award ID(s):
- 2309260
- PAR ID:
- 10597771
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review Physics Education Research
- Volume:
- 20
- Issue:
- 2
- ISSN:
- 2469-9896
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
[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 Society2025more » « less
-
The Survey of Physics Reasoning on Uncertainty Concepts in Experiments (SPRUCE) was designed to measure students’ proficiency with measurement uncertainty concepts and practices across ten different assessment objectives to help facilitate the improvement of laboratory instruction focused on this important topic. To ensure the reliability and validity of this assessment, we conducted a comprehensive statistical analysis using classical test theory. This analysis includes an evaluation of the test as a whole, as well as an in-depth examination of individual items and assessment objectives. We make use of a previously reported on scoring scheme involving pairing items with assessment objectives, creating a new unit for statistical analysis referred to as a “couplet.” The findings from our analysis provide evidence for the reliability and validity of SPRUCE as an assessment tool for undergraduate physics labs. This increases both instructors’ and researchers’ confidence in using SPRUCE for measuring students’ proficiency with measurement uncertainty concepts and practices to ultimately improve laboratory instruction. Additionally, our results using couplets and assessment objectives demonstrate how these can be used with traditional classic test theory analysis. Published by the American Physical Society2024more » « less
-
[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] We discuss an investigation of student sensemaking and reasoning in the context of degenerate perturbation theory (DPT) in quantum mechanics. We find that advanced undergraduate and graduate students in quantum physics courses often struggled with expertlike sensemaking and reasoning to solve DPT problems. The sensemaking and reasoning were particularly challenging for students as they tried to integrate physical and mathematical concepts to solve DPT problems. Their sensemaking showed local coherence but lacked global consistency with different knowledge resources getting activated in different problem-solving tasks even if the same concepts were applicable. Depending upon the issues involved in the DPT problems, students were sometimes stuck in the “physics mode” or “math mode” and found it challenging to coordinate and integrate the physics and mathematics appropriately to solve quantum mechanics problems involving DPT. Their sensemaking shows the use of various reasoning primitives. It also shows that some advanced students struggled with self-monitoring and checking their answers to make sure they were consistent across different problems. Some also relied on memorized information, invoked authority, and did not make appropriate connections between their DPT problem solutions and the outcomes of experiments. Advanced students in quantum mechanics often displayed analogous patterns of challenges in sensemaking and reasoning as those that have been found in introductory physics. Student sensemaking and reasoning show that these advanced students are still developing expertise in this novel quantum physics domain as they learn to integrate physical and mathematical concepts. Published by the American Physical Society2024more » « less
-
[This paper is part of the Focused Collection in Artificial Intelligence Tools in Physics Teaching and Physics Education Research.] One of the greatest weaknesses of physics education research is the paucity of research on graduate education. While there are a growing number of investigations of graduate student degree progress and admissions, there are very few investigations of at the graduate level. Additionally, existing studies of learning in physics graduate programs frequently focus on content knowledge rather than professional skills such as problem solving. Given that over 90% of physics Ph.D. graduates report solving technical problems regularly in the workplace, we sought to develop an assessment to measure how well graduate programs are training students to solve problems. Using a framework that characterizes expert-like problem-solving skills as a set of decisions to be made, we developed and validated such an assessment in graduate quantum mechanics (QM) following recently developed design frameworks for measuring problem solving and best practices for assessment validation. We collected validity evidence through think-aloud interviews with practicing physicists and physics graduate students, as well as written solutions provided by physics graduate and undergraduate students. The assessment shows strong potential in differentiating novice and expert problem solving in QM and showed reliability in repeated testing with similar populations. These results show the promise of measuring expert decision making in graduate QM and provide baseline measurements for future educational interventions to more effectively teach these skills. Published by the American Physical Society2025more » « less
