**December 2021 Issue,**

**Volume 89, No. 12**

#### EDITORIAL

In this issue: December 2021 by Tyler Engstrom, John Essick, Claire A. Marrache-Kikuchi, Beth Parks, B. Cameron Reed and Timothy D. Wiser. DOI: 10.1119/5.0075152

#### RESOURCE LETTERS

Resource Letter BP-1: Biological physics by Raghuveer Parthasarathy. DOI: 10.1119/5.0060279

Biological physics includes a huge breadth of research: The annual meeting of the Biophysical Society typically attracts more than 6000 researchers. This Resource Letter is intended to provide some footholds for physicists who would like to learn more about the field in general, with a particular focus on subcellular structure and function, cell-scale mechanics and organization, collective behaviors and embryogenesis, genetic networks, and ecological dynamics.

#### PAPERS

Using smartphone photographs of the Moon to acquaint students with non-Euclidean geometry by Hugo Caerols, Rodrigo A. Carrasco and Felipe A. Asenjo. DOI: 10.1119/10.0006156

Concepts of non-Euclidean geometry can be challenging for beginning students. This paper describes exercises in which students acquire their own photographs of the Moon with a smartphone and a small telescope. Freely-available software is used to make measurements of the diameters of craters, lengths of mountain chains, and areas of maria. “Flat” Euclidean-based measurements can have significant errors that are corrected by considering geodesics and spherical trigonometry. The exercises are suitable for undergraduate students, or, if the mathematical relationships are provided, they can be adapted to upper-level high-school students.

Measuring the balance of the world's largest machine by William H. Baird. DOI: 10.1119/10.0005989

This paper provides a way for students to link concepts in electronics and electromagnetism to real-world measurements, showing how small variations in the 60 Hz frequency standard occur when the power provided by generators isn’t exactly balanced by the power demand. The author goes on to describe experiments in which the frequency variations (including corrections made by grid operators) can be observed across time and space. The above link will also take the reader to the article’s video abstract.

On the ubiquity |of classical harmonic oscillators and a universal equation for the natural |frequency of a perturbed syste by J. J. Bissell. DOI: 10.1119/10.0005948

Simple harmonic motion re-appears throughout physics. Beginning students usually analyze such systems by considering the time dependence of small displacements of a system from a point of stable equilibrium, while more advanced students learn the techniques of Lagrangian dynamics. This paper develops a new approach to harmonic motion via a two-variable Taylor-series expansion of a system’s total energy. This approach results in a very appealing universal expression for the oscillation frequency of a system that can be applied to both mechanical and electrical systems alike without having to invoke analogies. Because this method involves no mathematics beyond partial derivatives, it opens up a wide variety of more advanced problems for lower-level students.

An exact solution for a particle in a velocity-dependent force field by Julio M. Yáñez, Gonzalo Gutiérrez, Felipe González-Cataldo and David Laroze. DOI: 10.1119/10.0005992

Using rotation operators enables solving a common class of differential equations in which the force depends on the velocity, including the Lorentz force and the Coriolis force, and helps to show their commonalities.

Classical and quantum confocal parabolic billiards by Bárbara K. Villarreal-Zepeda, Héctor M. Iga-Buitrón and Julio C. Gutiérrez-Vega. DOI: 10.1119/10.0006018

Particles confined within rigid 2-D boundaries (billiards) are used as model problems in mechanics because they illustrate fundamental properties (quantization, degeneracy, conservation of angular momentum) and they allow students to explore the connection between classical and quantum solutions. This manuscript introduces a solvable geometry (confocal parabolas) that can be solved both classically and quantum mechanically, and it provides a useful model system for computational physics.

The harmonic quantum Szilárd engine by P. C. W. Davies, Logan Thomas and George Zahariade. DOI: 10.1119/10.0005946

The engine Leó Szilárd proposed in 1929 is a version of Maxwell’s demon where a single particle is confined within a potential. A demon inserts a mobile barrier within this potential, determines which side contains the particle, and then expands that side isothermally, so as to extract useful work without having to provide any energy to system. Thus, the demon seems to violate the second law of thermodynamics. The paradox is lifted by acknowledging that gathering information on the particle’s whereabouts is not cost-free. This paper explores the quantum Szilárd engine where the particle is placed in a harmonic potential. Remarkably, in this case, all calculations can be performed analytically, rendering the study of this paradox accessible to graduate or advanced undergraduate students.

Single-, double-, and triple-slit diffraction of molecular matter waves by Christian Brand, Stephan Troyer, Christian Knobloch, Ori Cheshnovsky and Markus Arndt. DOI: 10.1119/5.0058805

At what length scale does quantum mechanics turn into classical mechanics? Experimentalists keep successfully diffracting larger and larger objects through slits, with no sign of stopping. This article explores the physics of diffracting entire molecules—in this case phthalocyanine—through nanofabricated slits and gratings. While the basic diffraction process will be familiar to students and teachers of wave optics, the relatively slow speed of molecules and electrostatic interactions with the grating add interesting twists to the physics. A number of example homework problems (and solutions!) are provided with the Supplemental Material.

#### ADVANCED TOPICS

Williamson theorem in classical, quantum, and statistical physics by F. Nicacio. DOI: 10.1119/10.0005944

The Williamson theorem provides a method to determine the change of coordinates in phase space that will reveal the normal modes and eigenfrequencies of a system. But it also has broader applicability in quantum mechanics and statistical mechanics. While advanced undergraduates will be able to follow the mathematical formalism, the theorem will be most useful in graduate-level instruction.

#### INSTRUCTIONAL LABORATORIES AND DEMONSTRATIONS

Ultrafast optics |with a mode-locked erbium fiber laser in the undergraduate laboratory by Daniel Upcraft, Andrew Schaffer, Connor Fredrick, Daniel Mohr, Nathan Parks, Andrew Thomas, Ella Sievert, Austin Riedemann, Chad W. Hoyt and R. Jason Jones. DOI: 10.1119/10.0005890

The Williamson theorem provides a method to determine the change of coordinates in phase space that will reveal the normal modes and eigenfrequencies of a system. But it also has broader applicability in quantum mechanics and statistical mechanics. While advanced undergraduates will be able to follow the mathematical formalism, the theorem will be most useful in graduate-level instruction.

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