Student ability to distinguish between superposition states and mixed states in quantum mechanics

Passante, Gina; Emigh, Paul J.; Shaffer, Peter S.

doi:10.1103/physrevstper.11.020135

Cited by 26 publications

(26 citation statements)

References 17 publications

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“…They also did not take into account the phase shifts of each photon path component and how the phase difference between the U and L paths causes constructive and destructive interference of single photons at the detectors. Students' conceptual difficulties involving superposition states in quantum mechanics has been found in other contexts as well [7].…”

Section: Students' Conceptual Difficultiesmentioning

confidence: 99%

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Investigating and improving student understanding of quantum mechanics in the context of single photon interference

Marshman

Singh

2017

Phys. Rev. Phys. Educ. Res.

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Single photon experiments involving a Mach-Zehnder interferometer can illustrate the fundamental principles of quantum mechanics, e.g., the wave-particle duality of a single photon, single photon interference, and the probabilistic nature of quantum measurement involving single photons. These experiments explicitly make the connection between the abstract quantum theory and concrete laboratory settings and have the potential to help students develop a solid grasp of the foundational issues in quantum mechanics. Here we describe students' conceptual difficulties with these topics in the context of MachZehnder interferometer experiments with single photons and how the difficulties found in written surveys and individual interviews were used as a guide in the development of a Quantum Interactive Learning Tutorial (QuILT). The QuILT uses an inquiry-based approach to learning and takes into account the conceptual difficulties found via research to help upper-level undergraduate and graduate students learn about foundational quantum mechanics concepts using the concrete quantum optics context. It strives to help students learn the basics of quantum mechanics in the context of single photon experiment, develop the ability to apply fundamental quantum principles to experimental situations in quantum optics, and explore the differences between classical and quantum ideas in a concrete context. We discuss the findings from in-class evaluations suggesting that the QuILT was effective in helping students learn these abstract concepts.

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Section: Students' Conceptual Difficultiesmentioning

confidence: 99%

“…[1][2][3][4][5][6]), and focused on diverse pedagogical approaches for helping students learn quantum mechanics better (see, e.g., Refs. [7][8][9][10][11][12][13][14]). …”

Section: Introductionmentioning

confidence: 99%

Investigating and improving student understanding of quantum mechanics in the context of single photon interference

Marshman

Singh

2017

Phys. Rev. Phys. Educ. Res.

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“…In addition, relative phase and various setups of the Stern-Gerlach experiment are taught extensively in the sophomore-level quantum mechanics course. The task was inspired by questions used by Passante et al to probe student ability to distinguish superposition states from mixed states [21].…”

Section: Observational Experiment: Studymentioning

confidence: 99%

“…The results showed that many students confuse Hilbert space with physical space and have difficulty reasoning about what components of spin need to be measured. Passante et al [21] probed whether or not students recognize that position states and mixed states are different experimentally, as well as the reasoning that students used to justify their answers. They found that many students do not recognize that superposition states and mixed states are experimentally distinguishable.…”

Section: Introductionmentioning

confidence: 99%

Probing student reasoning in relating relative phase and quantum phenomena

Wan

Emigh

Shaffer

2019

Phys. Rev. Phys. Educ. Res.

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In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore-and junior-level students' reasoning patterns in relating relative phases and real-world quantum phenomena. The investigation involved one observational experiment and three testing experiments, during which we formulated and tested three hypotheses that allow us to gain insights into why students have difficulty recognizing the measurable effects of relative phases. We found that, in both spin-1=2 and infinite square well contexts, many students do not recognize that quantum states differing only by a relative phase are experimentally distinguishable. Moreover, student ability to recognize the measurable effects of relative phase does not improve when given (i) a task that specifically prompts students to compare the probabilities for a particular observable and (ii) a task that does not require taking inner products or changing basis. We also examined the extent to which lacking proficiency with complex numbers may have hindered student understanding of relative phase. The data indicate that most students are proficient with complex numbers. These findings suggest that many students do not, in fact, recognize the purpose of using complex numbers in superposition states. We discuss possible explanations for why students do not seem to recognize this purpose, and we also provide suggestions for future avenues of research.

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“…Quantum mechanics (QM) is a particularly challenging subject for upper-level undergraduate and graduate students in physics [1][2][3][4]. Guided by research studies conducted to identify student difficulties with QM and findings of cognitive research, we have been developing a set of researchbased learning tools including the Quantum Interactive Learning Tutorials (QuILTs) [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Developing and evaluating an interactive tutorial on degenerate perturbation theory

Keebaugh¹,

Marshman²,

Singh³

2016

2016 Physics Education Research Conference Proceedings

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We discuss an investigation of student difficulties with degenerate perturbation theory (DPT) carried out in advanced quantum mechanics courses by administering free-response and multiple-choice questions and conducting individual interviews with students. We find that students share many common difficulties related to this topic. We used the difficulties found via research as resources to develop and evaluate a Quantum Interactive Learning Tutorial (QuILT) which strives to help students develop a functional understanding of DPT. We discuss the development of the DPT QuILT and its preliminary evaluation in the undergraduate and graduate courses.

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Student ability to distinguish between superposition states and mixed states in quantum mechanics

Cited by 26 publications

References 17 publications

Investigating and improving student understanding of quantum mechanics in the context of single photon interference

Investigating and improving student understanding of quantum mechanics in the context of single photon interference

Probing student reasoning in relating relative phase and quantum phenomena

Developing and evaluating an interactive tutorial on degenerate perturbation theory

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