American Association of Physics Teachers: American Journal of Physics: Table of Contents
Table of Contents for American Journal of Physics. List of articles from both the latest and ahead of print issues.
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American Association of Physics Teachers: American Journal of Physics: Table of Contents
American Association of Physics Teachers
enUS
American Journal of Physics
https://aapt.scitation.org/na101/home/literatum/publisher/aip/journals/content/ajp/2021/ajp.2021.89.issue12/ajp.2021.89.issue12/20211122/ajp.2021.89.issue12.cover.jpg
https://aapt.scitation.org/loi/ajp?af=R&feed=mostrecent

In this issue: December 2021
https://aapt.scitation.org/doi/10.1119/5.0075152?af=R&feed=mostrecent
American Journal of Physics, <a href="https://aapt.scitation.org/toc/ajp/89/12">Volume 89, Issue 12</a>, Page 10691070, December 2021. <br/>
American Journal of Physics, Volume 89, Issue 12, Page 10691070, December 2021. <br/>
In this issue: December 2021
10.1119/5.0075152
American Journal of Physics
20211122T12:51:45Z
© 2021 Author(s).
Tyler Engstrom
John Essick
Claire A. MarracheKikuchi
Beth Parks
B. Cameron Reed
Timothy D. Wiser

Resource Letter BP1: Biological physics
https://aapt.scitation.org/doi/10.1119/5.0060279?af=R&feed=mostrecent
American Journal of Physics, <a href="https://aapt.scitation.org/toc/ajp/89/12">Volume 89, Issue 12</a>, Page 10711078, December 2021. <br/>This Resource Letter provides an overview of the literature in biological physics, a vast, active, and expanding field that links the phenomena of the living world to the tools and perspectives of physics. While no survey of this area could be complete, this list and commentary are intended to help provide an entry point for upperlevel undergraduates, graduate students, researchers new to biophysics, or workers in subfields of biophysics who wish to expand their horizons. Topics covered include subcellular structure and function, cellscale mechanics and organization, collective behaviors and embryogenesis, genetic networks, and ecological dynamics.
American Journal of Physics, Volume 89, Issue 12, Page 10711078, December 2021. <br/>This Resource Letter provides an overview of the literature in biological physics, a vast, active, and expanding field that links the phenomena of the living world to the tools and perspectives of physics. While no survey of this area could be complete, this list and commentary are intended to help provide an entry point for upperlevel undergraduates, graduate students, researchers new to biophysics, or workers in subfields of biophysics who wish to expand their horizons. Topics covered include subcellular structure and function, cellscale mechanics and organization, collective behaviors and embryogenesis, genetic networks, and ecological dynamics.
Resource Letter BP1: Biological physics
10.1119/5.0060279
American Journal of Physics
20211122T12:51:51Z
© 2021 Author(s).
Raghuveer Parthasarathy

Using smartphone photographs of the Moon to acquaint students with nonEuclidean geometry
https://aapt.scitation.org/doi/10.1119/10.0006156?af=R&feed=mostrecent
American Journal of Physics, <a href="https://aapt.scitation.org/toc/ajp/89/12">Volume 89, Issue 12</a>, Page 10791085, December 2021. <br/>NonEuclidean geometry can be taught to students using astronomical images. By using photographs of the Moon taken with a smartphone through a simple telescope, we were able to introduce these concepts to highschool students and lowerlevel college students. We teach students how to calculate lengths of mountain ranges or areas of craters on the Moon's surface and introduce ideas of geodesics and spherical triangles. Students can see that accurate measurements cannot be obtained using flat geometry. Instead, by using threedimensional curved geometry, estimates of lengths and areas can be computed with less than 4% error.
American Journal of Physics, Volume 89, Issue 12, Page 10791085, December 2021. <br/>NonEuclidean geometry can be taught to students using astronomical images. By using photographs of the Moon taken with a smartphone through a simple telescope, we were able to introduce these concepts to highschool students and lowerlevel college students. We teach students how to calculate lengths of mountain ranges or areas of craters on the Moon's surface and introduce ideas of geodesics and spherical triangles. Students can see that accurate measurements cannot be obtained using flat geometry. Instead, by using threedimensional curved geometry, estimates of lengths and areas can be computed with less than 4% error.
Using smartphone photographs of the Moon to acquaint students with nonEuclidean geometry
10.1119/10.0006156
American Journal of Physics
20211122T12:51:50Z
© 2021 Author(s).
Hugo Caerols
Rodrigo A. Carrasco
Felipe A. Asenjo

Measuring the balance of the world's largest machine
https://aapt.scitation.org/doi/10.1119/10.0005989?af=R&feed=mostrecent
American Journal of Physics, <a href="https://aapt.scitation.org/toc/ajp/89/12">Volume 89, Issue 12</a>, Page 10861093, December 2021. <br/>10.1119/10.0005989.1The electrical power grid has been described as the largest machine in the world. Although we customarily assume our electrical outlets provide a steady sinusoidal voltage with a frequency of 60 Hz (in North America), the variations from that ideal are easy to observe using the methods described in this article. These frequency variations are important since, as can be shown with introductorylevel physics concepts, they arise when power generation and usage are not balanced on the electrical grid. The challenge of balancing the electrical grid will increase over the coming years as we adopt more sustainable but less predictable energy sources, and this connection to one of our current societal challenges makes this project interesting to students.
American Journal of Physics, Volume 89, Issue 12, Page 10861093, December 2021. <br/>10.1119/10.0005989.1The electrical power grid has been described as the largest machine in the world. Although we customarily assume our electrical outlets provide a steady sinusoidal voltage with a frequency of 60 Hz (in North America), the variations from that ideal are easy to observe using the methods described in this article. These frequency variations are important since, as can be shown with introductorylevel physics concepts, they arise when power generation and usage are not balanced on the electrical grid. The challenge of balancing the electrical grid will increase over the coming years as we adopt more sustainable but less predictable energy sources, and this connection to one of our current societal challenges makes this project interesting to students.
Measuring the balance of the world's largest machine
10.1119/10.0005989
American Journal of Physics
20211122T12:51:48Z
© 2021 Author(s).
William H. Baird

On the ubiquity of classical harmonic oscillators and a universal equation for the natural frequency of a perturbed system
https://aapt.scitation.org/doi/10.1119/10.0005948?af=R&feed=mostrecent
American Journal of Physics, <a href="https://aapt.scitation.org/toc/ajp/89/12">Volume 89, Issue 12</a>, Page 10941102, December 2021. <br/>A new perspective on the ubiquity of classical harmonic oscillators is presented based on the twovariable Taylor expansion of a perturbed system's total energy [math], where q(t) is the system displacement as a function of time t and [math]. This generalised approach permits derivation of the lossless oscillator equation from energy arguments only, yielding a universal equation for the oscillation frequency [math] which may be applied to arbitrary systems without the need to form systemspecific linearised models. As illustrated by a range of examples, this perspective gives a unifying explanation for the prevalence of harmonic oscillators in classical physics, can be extended to include damping effects and driving forces, and is a powerful tool for simplifying the analyses of perturbed systems.
American Journal of Physics, Volume 89, Issue 12, Page 10941102, December 2021. <br/>A new perspective on the ubiquity of classical harmonic oscillators is presented based on the twovariable Taylor expansion of a perturbed system's total energy [math], where q(t) is the system displacement as a function of time t and [math]. This generalised approach permits derivation of the lossless oscillator equation from energy arguments only, yielding a universal equation for the oscillation frequency [math] which may be applied to arbitrary systems without the need to form systemspecific linearised models. As illustrated by a range of examples, this perspective gives a unifying explanation for the prevalence of harmonic oscillators in classical physics, can be extended to include damping effects and driving forces, and is a powerful tool for simplifying the analyses of perturbed systems.
On the ubiquity of classical harmonic oscillators and a universal equation for the natural frequency of a perturbed system
10.1119/10.0005948
American Journal of Physics
20211122T12:51:45Z
© 2021 Author(s).
J. J. Bissell

An exact solution for a particle in a velocitydependent force field
https://aapt.scitation.org/doi/10.1119/10.0005992?af=R&feed=mostrecent
American Journal of Physics, <a href="https://aapt.scitation.org/toc/ajp/89/12">Volume 89, Issue 12</a>, Page 11031112, December 2021. <br/>We revisit the classical mechanics problem of a particle moving under the influence of a force that depends on its velocity. Using the properties of the rotation matrix and associated operators, we show that it is possible to find an exact analytical solution to a number of problems where the differential equation of motion depends on the velocity. First, we apply our method to the wellknown cases of a particle under the influence of the Lorentz force and Coriolis force, providing the complete analytical solution in each case for the motion of the particle in three dimensions. We also show that the complete solution can be obtained when the centrifugal force is included, showing the applicability to cases where there is simultaneous dependence on the position and velocity. This method, which is not currently discussed in a typical course in elementary mechanics, provides an alternative approach to the traditional methods that are used to solve these types of problems.
American Journal of Physics, Volume 89, Issue 12, Page 11031112, December 2021. <br/>We revisit the classical mechanics problem of a particle moving under the influence of a force that depends on its velocity. Using the properties of the rotation matrix and associated operators, we show that it is possible to find an exact analytical solution to a number of problems where the differential equation of motion depends on the velocity. First, we apply our method to the wellknown cases of a particle under the influence of the Lorentz force and Coriolis force, providing the complete analytical solution in each case for the motion of the particle in three dimensions. We also show that the complete solution can be obtained when the centrifugal force is included, showing the applicability to cases where there is simultaneous dependence on the position and velocity. This method, which is not currently discussed in a typical course in elementary mechanics, provides an alternative approach to the traditional methods that are used to solve these types of problems.
An exact solution for a particle in a velocitydependent force field
10.1119/10.0005992
American Journal of Physics
20211122T12:51:43Z
© 2021 Author(s).
Julio M. Yáñez
Gonzalo Gutiérrez
Felipe GonzálezCataldo
David Laroze

Classical and quantum confocal parabolic billiards
https://aapt.scitation.org/doi/10.1119/10.0006018?af=R&feed=mostrecent
American Journal of Physics, <a href="https://aapt.scitation.org/toc/ajp/89/12">Volume 89, Issue 12</a>, Page 11131122, December 2021. <br/>The classical and quantum description of a free particle moving inside a confocal parabolic billiard is studied. From a classical approach, we derive the characteristic equations for periodic trajectories, discuss the Poincaré maps, and explore interesting geometrical properties of the orbits inside the billiard. From a quantum description, we determine the eigenstates and energy spectrum of the confined particle. The confocal parabolic billiard is an integrable system that exhibits two degrees of freedom and two constants of motion. The way to establish a correspondence between the classical and quantum solutions is by equating the constants of motion for both descriptions. The parabolic billiard provides a wellmotivated and relatively straightforward example of the Hamilton–Jacobi theory in a way that is seldom discussed in the undergraduate curriculum.
American Journal of Physics, Volume 89, Issue 12, Page 11131122, December 2021. <br/>The classical and quantum description of a free particle moving inside a confocal parabolic billiard is studied. From a classical approach, we derive the characteristic equations for periodic trajectories, discuss the Poincaré maps, and explore interesting geometrical properties of the orbits inside the billiard. From a quantum description, we determine the eigenstates and energy spectrum of the confined particle. The confocal parabolic billiard is an integrable system that exhibits two degrees of freedom and two constants of motion. The way to establish a correspondence between the classical and quantum solutions is by equating the constants of motion for both descriptions. The parabolic billiard provides a wellmotivated and relatively straightforward example of the Hamilton–Jacobi theory in a way that is seldom discussed in the undergraduate curriculum.
Classical and quantum confocal parabolic billiards
10.1119/10.0006018
American Journal of Physics
20211122T12:51:47Z
© 2021 Author(s).
Bárbara K. VillarrealZepeda
Héctor M. IgaBuitrón
Julio C. GutiérrezVega

The harmonic quantum Szilárd engine
https://aapt.scitation.org/doi/10.1119/10.0005946?af=R&feed=mostrecent
American Journal of Physics, <a href="https://aapt.scitation.org/toc/ajp/89/12">Volume 89, Issue 12</a>, Page 11231131, December 2021. <br/>The Szilárd engine is a mechanism (akin to Maxwell's demon) for converting information into energy, which seemingly violates the second law of thermodynamics. Originally a classical thought experiment, it was extended to a quantized treatment by Zurek. Here, we examine a new, elegant model of a quantum Szilárd engine by replacing the traditional rigid box with a harmonic potential, extending the scope of the model. Remarkably, almost all calculations are exact. This article is suitable for students, researchers, and educators interested in the conceptual links among information, entropy, and quantum measurement.
American Journal of Physics, Volume 89, Issue 12, Page 11231131, December 2021. <br/>The Szilárd engine is a mechanism (akin to Maxwell's demon) for converting information into energy, which seemingly violates the second law of thermodynamics. Originally a classical thought experiment, it was extended to a quantized treatment by Zurek. Here, we examine a new, elegant model of a quantum Szilárd engine by replacing the traditional rigid box with a harmonic potential, extending the scope of the model. Remarkably, almost all calculations are exact. This article is suitable for students, researchers, and educators interested in the conceptual links among information, entropy, and quantum measurement.
The harmonic quantum Szilárd engine
10.1119/10.0005946
American Journal of Physics
20211122T12:51:50Z
© 2021 Author(s).
P. C. W. Davies
Logan Thomas
George Zahariade

Single, double, and tripleslit diffraction of molecular matter waves
https://aapt.scitation.org/doi/10.1119/5.0058805?af=R&feed=mostrecent
American Journal of Physics, <a href="https://aapt.scitation.org/toc/ajp/89/12">Volume 89, Issue 12</a>, Page 11321138, December 2021. <br/>Even 100 years after its introduction by Louis de Broglie, the wavenature of matter is often regarded as a mindboggling phenomenon. To give an intuitive introduction to this field, we here discuss the diffraction of massive molecules through a single, a double, and a triple slit, as well as a nanomechanical grating. While the experiments are in good agreement with undergraduate textbook predictions, we also observe pronounced differences resulting from the molecules' mass and internal complexity. The molecules' polarizability causes an attractive van der Waals interaction with the slit walls, which can be modified by rotating the nanomechanical mask with respect to the molecular beam. The text is meant to introduce students and teachers to the concepts of molecule diffraction, supported by problems and solutions that can be discussed in class.
American Journal of Physics, Volume 89, Issue 12, Page 11321138, December 2021. <br/>Even 100 years after its introduction by Louis de Broglie, the wavenature of matter is often regarded as a mindboggling phenomenon. To give an intuitive introduction to this field, we here discuss the diffraction of massive molecules through a single, a double, and a triple slit, as well as a nanomechanical grating. While the experiments are in good agreement with undergraduate textbook predictions, we also observe pronounced differences resulting from the molecules' mass and internal complexity. The molecules' polarizability causes an attractive van der Waals interaction with the slit walls, which can be modified by rotating the nanomechanical mask with respect to the molecular beam. The text is meant to introduce students and teachers to the concepts of molecule diffraction, supported by problems and solutions that can be discussed in class.
Single, double, and tripleslit diffraction of molecular matter waves
10.1119/5.0058805
American Journal of Physics
20211122T12:51:46Z
© 2021 Author(s).
Christian Brand
Stephan Troyer
Christian Knobloch
Ori Cheshnovsky
Markus Arndt

Williamson theorem in classical, quantum, and statistical physics
https://aapt.scitation.org/doi/10.1119/10.0005944?af=R&feed=mostrecent
American Journal of Physics, <a href="https://aapt.scitation.org/toc/ajp/89/12">Volume 89, Issue 12</a>, Page 11391151, December 2021. <br/>In this work, we present (and encourage the use of) the Williamson theorem and its consequences in several contexts in physics. We demonstrate this theorem using only basic concepts of linear algebra and symplectic matrices. As an immediate application in the context of small oscillations, we show that applying this theorem reveals the normalmode coordinates and frequencies of the system in the Hamiltonian scenario. A modest introduction of the symplectic formalism in quantum mechanics is presented, using the theorem to study quantum normal modes and canonical distributions of thermodynamically stable systems described by quadratic Hamiltonians. As a last example, a more advanced topic concerning uncertainty relations is developed to show once more its utility in a distinct and modern perspective.
American Journal of Physics, Volume 89, Issue 12, Page 11391151, December 2021. <br/>In this work, we present (and encourage the use of) the Williamson theorem and its consequences in several contexts in physics. We demonstrate this theorem using only basic concepts of linear algebra and symplectic matrices. As an immediate application in the context of small oscillations, we show that applying this theorem reveals the normalmode coordinates and frequencies of the system in the Hamiltonian scenario. A modest introduction of the symplectic formalism in quantum mechanics is presented, using the theorem to study quantum normal modes and canonical distributions of thermodynamically stable systems described by quadratic Hamiltonians. As a last example, a more advanced topic concerning uncertainty relations is developed to show once more its utility in a distinct and modern perspective.
Williamson theorem in classical, quantum, and statistical physics
10.1119/10.0005944
American Journal of Physics
20211122T12:51:48Z
© 2021 Author(s).
F. Nicacio

Ultrafast optics with a modelocked erbium fiber laser in the undergraduate laboratory
https://aapt.scitation.org/doi/10.1119/10.0005890?af=R&feed=mostrecent
American Journal of Physics, <a href="https://aapt.scitation.org/toc/ajp/89/12">Volume 89, Issue 12</a>, Page 11521160, December 2021. <br/>We describe an ultrafast optics laboratory comprising a modelocked erbium fiber laser, autocorrelation measurements, and a freespace parallel grating dispersion compensation apparatus. The gain spectrum of Er fiber provides a broad bandwidth capable of supporting sub100 fs pulses centered near a wavelength of 1550 nm. The fiber laser design used here produces a train of pulses at a repetition rate of 55 MHz with pulse duration as short as 108 fs. The pulse duration is measured with a homebuilt autocorrelator using a simple Michelson interferometer that takes advantage of the twophoton nonlinear response of a common silicon photodiode. To compensate for temporal stretching of the short pulse due to group velocity dispersion in the fiber, an apparatus based on a pair of parallel gratings is used for pulse compression. A detailed part that lists in the supplementary material includes previously owned and common parts used by the telecommunications industry, which helps decrease costs of the laboratory. This provides a costeffective way to introduce the principles of ultrafast optics to undergraduate laboratories.
American Journal of Physics, Volume 89, Issue 12, Page 11521160, December 2021. <br/>We describe an ultrafast optics laboratory comprising a modelocked erbium fiber laser, autocorrelation measurements, and a freespace parallel grating dispersion compensation apparatus. The gain spectrum of Er fiber provides a broad bandwidth capable of supporting sub100 fs pulses centered near a wavelength of 1550 nm. The fiber laser design used here produces a train of pulses at a repetition rate of 55 MHz with pulse duration as short as 108 fs. The pulse duration is measured with a homebuilt autocorrelator using a simple Michelson interferometer that takes advantage of the twophoton nonlinear response of a common silicon photodiode. To compensate for temporal stretching of the short pulse due to group velocity dispersion in the fiber, an apparatus based on a pair of parallel gratings is used for pulse compression. A detailed part that lists in the supplementary material includes previously owned and common parts used by the telecommunications industry, which helps decrease costs of the laboratory. This provides a costeffective way to introduce the principles of ultrafast optics to undergraduate laboratories.
Ultrafast optics with a modelocked erbium fiber laser in the undergraduate laboratory
10.1119/10.0005890
American Journal of Physics
20211122T12:51:42Z
© 2021 Author(s).
Daniel Upcraft
Andrew Schaffer
Connor Fredrick
Daniel Mohr
Nathan Parks
Andrew Thomas
Ella Sievert
Austin Riedemann
Chad W. Hoyt
R. Jason Jones