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We discuss an investigation of student difficulties with Dirac notation in the context of a three-dimensional vector space and the validation and evaluation of a Quantum Interactive Learning Tutorial (QuILT) to improve student understanding of these concepts. We find that many upper-level undergraduate students in quantum mechanics courses have difficulties with Dirac notation even in the context of a three-dimensional vector space after traditional instruction. The QuILT uses analogical reasoning and builds on students’ prior knowledge of three-dimensional vectors in the familiar context of introductory mechanics to help students build a coherent understanding of Dirac notation in three dimensions before transitioning to the quantum mechanical context. We summarize the development of the QuILT and findings from its evaluations. We thank the National Science Foundation for support.


AAPT SM 20

Improving Student Understanding Of Dirac Notation by Using Analogical Reasoning in the Context of a Three-Dimensional Vector Space

upper-division physics

dirac notation

quantum mechanics

Join us in exploring emergent themes in PER as a scholarly endeavor and as a research community!  Since its inception, PER has served as a confluence of discipline, theory, research methodology, practice, and application.  How have these facets and the interplays among them been fruitful for physics education globally, regionally, locally, or otherwise?  And, how have our successes and interactions influenced the very nature of PER itself?
Following the lead of AAPT for the summer meeting, PERC 20/20 was virtual. Enjoy browsing the content.

PERC SM 20

Since its inception, PER has served as a confluence of discipline, theory, research methodology, practice, and application.  How have these facets and the interplays among them been fruitful for physics education globally, regionally, locally, or otherwise?  And, how have our successes and interactions influenced the very nature of PER itself?

technical paper

The 2020 AAPT Virtual Summer Meeting brought together physics educators from around the globe to learn about the latest in physics theory, research methodology and education from leaders in their field. The program featured plenary speakers, sessions, workshops and many special activities.

For more information please visit the 2020 AAPT Virtual Summer Meeting page at: https://www.aapt.org/Conferences/SM2020/index.cfm.


The 2020 AAPT Virtual Summer Meeting brought together physics educators from around the globe to learn about the latest in physics theory, research methodology and education from leaders in their field. 

Developing and Evaluating Quantum Mechanics Formalism and Postulates Survey

Student Difficulties with Operators Corresponding to Observables in Dirac Notation

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Here we focus on an investigation that suggests that, even though Dirac notation is used extensively, many advanced undergraduate and Ph.D. students in physics have difficulty expressing the identity operator and other Hermitian operators corresponding to physical observables in Dirac notation. We first describe the difficulties students have with expressing the identity operator and other Hermitian operators corresponding to observables in Dirac notation. We then discuss how the difficulties found via written surveys and individual interviews were used as a guide in the development and validation of a Quantum Interactive Learning Tutorial (QuILT) to help students develop a good grasp of these concepts. We also discuss the effectiveness of the QuILT based on in-class evaluations. We thank the National Science Foundation for support.

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Ask your colleagues how they learned to do research. Most of us learned how to do research by reading publications our advisor told us to read and discussing the research with the research group or the group leader. We basically learned by doing something similar to that which has been already done and failing. In the failing, we modified some part of what we were doing and tried again. In this presentation I will present what my students do in Junior Lab to learn about designing a lab, communicating the results, and decision making in the process. I will also share my evaluation of their actions and reflect upon this process.

Junior Physics Laboratory: Scientific Reasoning, Communication & Decision Making

Students’ self-efficacy, interest and identity in physics can influence their learning, performance and career decisions. Therefore, we investigated the impact of learning environment on male and female students’ physics self-efficacy, interest and identity in calculus-based introductory physics. Findings can be useful in creating equitable and inclusive learning environments in which all students can thrive. We thank the National Science Foundation for support.

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Developing and Evaluating Quantum Mechanics Formalism and Postulates Survey

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