Emily Marshman

Interactive tutorial to improve student understanding of single photon experiments involving a Mach–Zehnder interferometer

We have developed and evaluated a quantum interactive learning tutorial (QuILT) on a Mach–Zehnder interferometer with single photons to expose upper-level students in quantum mechanics courses to contemporary quantum optics applications. The QuILT strives to help students develop the ability to apply fundamental quantum principles to physical situations in quantum optics and explore the differences between classical and quantum ideas. The QuILT adapts visualization tools to help students build physical intuition about counter-intuitive quantum optics phenomena with single photons including a quantum eraser setup and focuses on helping them integrate qualitative and quantitative understanding. We discuss findings from in-class evaluations.

Developing an interactive tutorial on a Mach-Zehnder Interferometer with single photons

We are developing a Quantum Interactive Learning Tutorial (QuILT) on a Mach-Zehnder Interferometer with single photons to expose upper-level students in quantum mechanics courses to contemporary applications. The QuILT strives to help students develop the ability to apply fundamental quantum principles to physical situations and explore differences between classical and quantum ideas. The QuILT adapts visualization tools to help students build physical intuition about quantum phenomena and focuses on helping them integrate qualitative and quantitative understanding. We also discuss findings from a preliminary in-class evaluation.

Developing an Interactive Tutorial on a Quantum Eraser

We are developing a quantum interactive learning tutorial (QuILT) on a quantum eraser for students in upperlevel quantum mechanics. The QuILT exposes students to contemporary topics in quantum mechanics and uses a guided approach to learning. It adapts existing visualization tools to help students build physical intuition about quantum phenomena and strives to help them develop the ability to apply quantum principles in physical situations. The quantum eraser apparatus in the gedanken (thought) experiments and simulations that students learn from in the QuILT uses a MachZehnder Interferometer with single photons. We also discuss findings from a preliminary in-class evaluation.

Investigating Student Difficulties with Dirac Notation

Quantum mechanics is challenging even for advanced undergraduate and graduate students. Dirac notation is a convenient notation used extensively in quantum mechanics. We have been investigating the difficulties that the advanced undergraduate and graduate students have with Dirac notation. We administered written free response and multiple-choice questions to students and also conducted semi-structured individual interviews with 23 students using a think-aloud protocol to obtain a better understanding of the rationale behind their responses. We find that many students struggle with Dirac notation and they are not consistent in using this notation across various questions in a given test. In particular, whether they answer questions involving Dirac notation correctly or not is context dependent.

The impact of peer interaction on the responses to clicker questions in an upper-level quantum mechanics course

In this case study, we investigated the effectiveness of peer interaction on responses to in-class clicker questions in an upper-level quantum mechanics course. We analyzed student performance on clicker questions answered individually and then again after interaction with peers. We also analyzed student performance by topic. In general, the performance on the clicker questions improved after interaction with peers following individual clicker responses. We also find evidence of co-construction of knowledge in that students who did not answer the clicker questions individually were able to answer them correctly after discussion with peers. Finally, we discuss the trends in the percentage of students present in class who responded to the clicker questions in the allotted time as the semester progressed.

Student difficulties with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations

We administered written free-response and multiple-choice questions and conducted individual interviews to investigate the difficulties that upper-level undergraduate and graduate students have with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations. We find that students share common difficulties with translating a state vector written in Dirac notation to the wave function in position or momentum representation.

Analogous Patterns of Student Reasoning Difficulties in Introductory Physics and Upper- Level Quantum Mechanics

Very little is known about how the nature of expertise in introductory and advanced courses compares in knowledge-rich domains such as physics. We develop a framework to compare the similarities and differences between learning and patterns of student difficulties in introductory physics and quantum mechanics. Based upon our framework, we argue that the qualitative patterns of student reasoning difficulties in introductory physics bear a striking resemblance to those found for upper-level quantum mechanics. The framework can guide the design of teaching and learning tools.

Developing and evaluating an interactive tutorial on degenerate perturbation theory

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.

Student difficulties with determining expectation values in quantum mechanics

The expectation value of an observable is an important concept in quantum mechanics. However, upper-level undergraduate and graduate students in physics have both conceptual and procedural difficulties when determining the expectation value of physical observables, especially when using Dirac notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students. Here, we discuss the analysis of data on student difficulties when determining the expectation value.

Student difficulties with representations of quantum operators corresponding to observables

Dirac notation is used commonly in quantum mechanics. However, many upper-level undergraduate and graduate students in physics have difficulties with representations of quantum operators corresponding to observables especially when using Dirac notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students in advanced quantum mechanics courses. We discuss the analysis of data on the common difficulties found.