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The wave equation for electromagnetic waves, the Helmholtz equation, has the same form as the Schrodinger equation of quantum mechanics. We present the generation of optical beams in Mathieu modes, whose angular solution is the same as the wavefunction for the quantized pendulum. The light in such a mode is generated by a spatial light modulator and imaged by digital cameras. The intensity of the light in the far field is proportional to the probability of finding the pendulum bob as a function of angle. In this experiment students can investigate, quantization, wavefunction symmetry, probabilities and explore non-classical aspects of the quantum solutions. Superpositions can also produce wave-packets that resemble the classical motion. We also focus on states that approximate the harmonic oscillator.

AAPT WM 21

An Advanced Lab on the Quantum Pendulum

pendulum

quantum mechanics

advanced lab

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

poster

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My upper level Acoustics course was thrust into virtual mode. I designed a “do this at home” lab exercise which my students could perform with readily available equipment found at home. We did a quick study of the Helmholtz Resonator by using an empty 2 L soda bottle, a measuring cup, a ruler and a smartphone. By measuring the frequency with different amounts of water in the bottle, the students were able to extract a good value for the volume of the empty bottle from their graphical analysis of the data.&nbsp; (Many of them were surprised to discover that it is NOT 2.0 L.) As an assessment of their ability to extend the analysis, an exam question provided them with data for a small pendant-style ocarina, from which they were able to deduce the interior volume of the ocarina. Both the lab and the extension will be described.

A virtual Helmholtz Resonator lab

We conducted research on student difficulties used it as a guide to develop, validate and evaluate a quantum interactive learning tutorial (QuILT) on Larmor precession of spin to help students learn about time-dependence of expectation values in quantum mechanics. The QuILT builds on students' prior knowledge and strives to help them develop a good knowledge structure of relevant concepts. It adapts visualization tools to help students develop intuition about these topics and focuses on helping students integrate qualitative and quantitative understanding. Here, we summarize the development, validation and in-class evaluation. We thank the National Science Foundation for support.

Quantum Interactive Learning Tutorial on Larmor Precession of Spin

Just-in-Time Teaching (JiTT) is an instructional strategy involving feedback from students on pre-lecture activities in order to design in-class activities to build on the continuing feedback from students. We investigated the effectiveness of a JiTT approach, which included in-class concept tests using clickers in an upper-division quantum mechanics course. We analyzed student performance on pre-lecture reading quizzes, in-class clicker questions answered individually, and clicker questions answered after group discussion, and compared those performances with open-ended retention quizzes administered after all instructional activities on the same concepts. In general, compared to the reading quizzes, student performance improved when individual clicker questions were posed after lectures that focused on student difficulties found via electronic feedback. The performance on the clicker questions after group discussion following individual clicker question responses also showed improvement. We discuss some possible reasons for improved performance at various stages. We thank the National Science Foundation for support.

Just-in-Time Teaching and Peer Instruction Using Clickers in Quantum Mechanics

We describe the development, validation and in-class evaluation of a Quantum Interactive Learning Tutorial (QuILT) on quantum key distribution, a context which involves an exciting application of quantum mechanics. The protocol used in the QuILT uses single photons with non-orthogonal polarization states to generate a random shared key over a public channel for encrypting and decrypting information. The QuILT strives to help upper-level undergraduate students learn quantum mechanics using a simple two state system. It actively engages students in the learning process and helps them build links between the formalism and the conceptual aspects of quantum physics without compromising the technical content. The in-class evaluation suggests that the validated QuILT is helpful in improving students’ understanding of relevant concepts. We thank the National Science Foundation for support.

A Quantum Interactive Learning Tutorial on Quantum Key Distribution

We developed and validated a Quantum Interactive Learning Tutorial (QuILT) on 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 understandings. Findings will be presented from in-class implementation of the research-validated QuILT. We thank the National Science Foundation for support.

Quantum Interactive Learning Tutorial on Mach-Zehnder Interferometer with Single Photons

All measurements used in education should be fair, reliable and valid. Psychometrics is the field of study that concerns itself with the development of these measurements. Specifically psychometricians develop theories of measurement of both the development of instrument assessing individuals’ skills, abilities, attitudes and educational knowledge, as well as the general test theory behind said development. Psychometrics should guide the development of all measurements undertaken as part of education including classroom tests, quizzes and any other quantitative data collected as part of normal courses as well as the research-based assessments, such as conceptual learning assessment instruments (RbCLAIs). Unfortunately, the theory and methods of psychometrics are not well known or understood.&nbsp; In this poster, I will present the basics of psychometrics as well as common misunderstandings of the psychometrics involved in the development of RBCLAIs.&nbsp;

What Physics Education Researchers Needs to Know About Psychometrics

&nbsp;Most students find difficulty in visualizing 3D concepts in physics courses. Some of these include torque, circular motion, and moment of inertia. A solution to this issue is to present these concepts in augmented reality to allow for better visualization of them. The augmented reality activities presented in this project were created by a team of undergraduate physics and computer science students using the software Unity and the Merge Cube. We present a systematic process of creating and improving specialized apps that can be utilized in a classroom environment.

Developing Augmented Reality Modules to Teach Torque

This poster will showcase one of our Interactive video-enhanced tutorials (IVETs). IVETs involve web-based activities that lead students through a solution using expert-like problem-solving approaches. Under NSF funding we have developed and evaluated multiple IVETs for use with college students in introductory physics. This presentation will showcase one of our IVETs, namely Torque and Rotation, and provide details about its design features, which involve multimedia principles of learning and research on human learning and memory. The&nbsp;IVET’s impact on student problem-solving abilities will also be shared.

Impact of Torque and Rotation Tutorial on Student Problem-Solving Abilities

I describe the sequential development of an animated Desmos visualization of the wave-interference from two point-sources. Starting with static wavefronts with tunable parameters, I compute the superposition to obtain an interference pattern in the plane. I then introduce a screen where I compute the instantaneous waveform and power, then the time-averaged power. Along the way, I’ll share some Desmos tricks I learned in the process. &nbsp;

Using Desmos for Interactive Visualizations of Physics: Wave-Interference

In our algebra-based introductory physics sequence, we have exams that consist of multiple choice and traditional math problems. Students were able to solve the math problems as well as expected, but found multiple choice questions to be more challenging. Students often asked for an optimal way to study for these questions, but we weren’t sure how to answer. So we set out to investigate how students were studying for these exams and how those study habits changed as they progressed through the course. After three years of data collection, we have insight into the ways students prepare for introductory physics exams, how they perceive these study methods to have affected their exam scores, and the study methods actual exam helpfulness. Our hope is to help our current students succeed in the course by introducing them to study methods that have shown to be effective in the past.

An Advanced Lab on the Quantum Pendulum

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A virtual Helmholtz Resonator lab

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