These brief summaries are designed to help readers easily see which articles will be most valuable to them. The online version contains links to the articles.

Ioana A. Zelko, Charles Barclay, Tõnis Eenmäe, Taavet Kalda, Hara Papathanassiou, Nikita Poljakov, Gustavo A. Rojas, Tiit Sepp, Greg Stachowski, and Aniket Sule

91(11), p. 867

The 2020 Global e-Competition in Astronomy and Astrophysics was an international Olympiad that successfully moved to an online format with little time to prepare. In this article, the organizers share their experience, which illustrates successful strategies — and pitfalls to avoid — for common challenges of hybrid and online teaching: administering and grading online exams (in multiple languages across many time zones), developing engaging group projects for remote students, and cultivating student interest through challenging assignments. The resources developed for the competition and described here are freely available for use in your own classroom and should also help other faculty who run physics or astronomy competitions.

Thomas Gallot, Daniel Gau, and Rodrigo Garcıa-Tejera

91(11), p. 873

The Wilberforce pendulum is a classic physics demonstration involving a spring-mass system with coupled torsional and longitudinal oscillations. Here, the authors discuss the appropriate theoretical and experimental modifications necessary for exploring the system with smartphone sensors. This approach eliminates the traditional need for multiple sensors and results in acceleration-based measurements that differ from the typical displacement-based measurements.

Rod Cross

91(11), p. 879

A classic introductory physics problem involves the study of a one-dimensional elastic collision between a moving object and another, initially stationary, object. The final state can be completely determined because the two unknown final velocities can be found from two conservation equations (energy and momentum). Now, imagine the more complicated problem where a moving ball collides off center with two stationary balls (initially touching). In this situation, the number of conservation equations is not sufficient to completely determine the outcome. This article addresses these complications in a way that can be shared with undergraduate students, and collisions involving three and four balls are studied experimentally. Students and instructors will delight in seeing how a slight modification to an elementary problem results in rich physics.

Livia A. J. Guttieres, Marko D. Petrović, and James K. Freericks

91(11), p. 885

The authors present a highly adaptable computational project suitable for quantum mechanics courses. Teachers who want to reinforce concepts like time evolution and time-independent perturbation theory, who want their students to engage in computational research style thinking, or who want to add cutting edge concepts like compression algorithms to their curricula will all find useful suggestions in this paper.

Charles Torre

91(11), p. 893

Under a fixed boost to a new inertial frame of reference, the usual non-relativistic quantum mechanical wave function undergoes a change of phase. The manner in which this occurs can provide additional insight, in advanced undergraduate quantum mechanics and mathematical methods courses, on the nature of symmetries. The author shows that this transformation property is related to a time derivative term that arises when the corresponding classical Lagrangian is transformed. It turns out that one can indeed derive the change of phase by employing this alteration of the Lagrangian in a path integral approach to quantum mechanics.

Leo de Wit

91(11), p. 903

Feynman diagrams are both attractive visualizations of physical processes and powerful calculational tools used in quantum field theory, a subject traditionally taught at the graduate level. Because they are employed at the forefront of research, Feynman diagrams tend to inspire intense curiosity among undergraduate students. Undergraduates can easily learn recipes to use these diagrams, but a deeper understanding arises by learning where the diagrams come from and understanding their inner workings. In this paper, a few toy models are introduced that illustrate essential features of field theory and the construction of Feynman diagrams. We hope students and instructors will enjoy this pedagogical introduction to field theory scattering in a simplified context.

S. G. Arutunian, M. A. Aginian, A. V. Margaryan, M. Chung, and E. G. Lazareva

91(11), p. 913

In this article, the authors derive a set of linear differential equations for constructing electric field lines of a charged particle in arbitrary motion. In some cases, these equations yield simple analytic solutions and geometric constructions. The authors construct field lines for a linearly oscillating charge, synchrotron motion, and the “figure eight” motion of a charged particle moving under the influence of an electromagnetic plane wave, including highly relativistic motion in strong fields. Readers can generate their own field lines using a script in the supplementary online material.

Markus Deserno and O. Teoman Turgut

91(11), p. 923

How different is a thermal quantum system from a classical one? This article delves into the fascinating realm of quantum statistical mechanics and examines the leading-order quantum correction to the classical free energy. A new derivation of a famous formula (due to Wigner) is provided, and results are then illustrated using several familiar systems (the harmonic oscillator and the particle in a box). Students will find this article aids in building intuition about the differences between classical and quantum systems. Instructors may be inspired to assign extensions or generalizations of these results as student projects.

Wittaya Kanchanapusakit and Pattarapon Tanalikhit

91(11), p. 932

An object moving through fluid experiences drag force, and treating this drag force is a standard part of classical fluid dynamics. But what if the motion must be treated quantum mechanically? This paper derives the temperature dependence of the drag force for classical gases, Fermi gases, and Bose gases.

Flynn B. Darby, Michael Y. Hua, Oskari V. Pakari, Shaun D. Clarke, and Sara A. Pozzi

91(11), p. 936

A versatile experimental setup for carrying out a modern nuclear assay technique is presented. The experimental setup is described in detail, along with the nondestructive assay methods it makes possible. In addition, abundant references are given to fill in background knowledge and encourage further study. As demonstrated in the experiment, these assay methods provide the ability to distinguish special nuclear materials (such as plutonium and enriched uranium) from other neutron sources. Such comparisons can help inspectors spot clandestine attempts to “relocate” fission sources by replacing them with sources that undergo (alpha, neutron) reactions. This paper will be of interest to instructional laboratory instructors wishing to adopt an up-to-date nuclear physics experiment as well as to those looking to learn more about nuclear nonproliferation techniques.

Xi-Jun Ren

91(11), p. 946

In classical mechanics, a particle experiencing a constant force (a linear potential) is both simple to analyze and fundamentally important. The corresponding quantum problem is surprisingly difficult and has been approached in a variety of ways in the literature. This short note employs momentum space to present a clear and straightforward derivation of the propagator and serves as a complement to other approaches. We hope that readers will enjoy a heightened understanding after examining the problem through this alternate lens.