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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.

AAPT SM 20

Investigating and improving student understanding of quantum mechanical observables and their corresponding operators in Dirac notation

learning tools

hermitian operator

student difficulties

quantum mechanics

quilt

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. 

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Investigating and improving student understanding of quantum mechanical observables and their corresponding operators in Dirac notation

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