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.

Regular readers will note the temporary increase in the length of the issue as we try to decrease the backlog of manuscripts. We think the end is in sight.

Siddharth Bhatnagar, Jayanth P. Vyasanakere, and Jayant Murthy

89(5), p. 454

In this paper, the authors develop a purely geometric method for locating an “unknown” planet by using location data for all other planets in the solar system. The method is applied to determining the orbit of Neptune from data for the Sun and the seven planets that were known at the time of the actual discovery of Neptune in 1846. This method is suitable for presentation in an advanced dynamics class.

Keith Zengel

89(5), p. 459

The behavior of a ball rolling inside a tilted cylinder follows a variety of intriguing paths that can be understood with only intermediate-level mechanics. The link above will also take the reader to the article's video abstract.

L. Martínez-Balbuena, A. Arteaga-Jiménez, E. Hernández-Zapata, and E. Urrutia-Buñuelos

89(5), p. 465

In a paper directed at undergraduates interested in biophysics, elastic energy is shown to dominate the equilibrium shapes of red blood cells and to explain the shape of those cells. The mathematics of the needed geometry for the curvature of two-dimensional surfaces is developed within the paper.

Martín Monteiro, Cecila Stari, Cecila Cabeza, and Arturo C. Martí

89(5), p. 477

Mobile phone sensors such as accelerometers can quickly provide very large data-sets that introductory physics students will enjoy using to better understand statistical errors.

Matthew J. Filipovich and Stephen Hughes

89(5), p. 482

Computing the fields generated by moving electrical charges is a common element of higher-level electromagnetism classes, but such fields can be difficult to visualize due to the complexity of the expressions involved. This paper describes and presents results from a computer code for directly calculating the fields and potentials of moving charges and currents. Appropriate for use in upper-level undergraduate and graduate electromagnetism classes.

Alexander E. Krosney, Michael Lang, Jakob J. Weirathmueller, and Christopher P. Bidinosti

89(5), p. 490

For low frequencies, penetration of a magnetic field through a conductor is governed by a diffusion equation. The authors study this phenomenon analytically, using the Laplace transform; and experimentally, using simple apparatus that can be found in a typical undergraduate teaching laboratory. Agreement between theory and experiment is very good, making the lab exercise ideal for studying the skin effect, eddy currents, and magnetic shielding.

Katsunori Mita

89(5), p. 500

Schrödinger's equation is more often than not considered to be a wave equation for the wave function. How strange! It actually looks more like a diffusion equation. This paper explores the implications of this point of view. The authors show that Schrödinger's equation then amounts to equations of motion and conservation for a probability density fluid. You will get a new perspective on classic undergraduate quantum mechanics problems: a particle in a box, Gaussian wave packets, the harmonic oscillator, and a mind-boggling quantum mechanical soliton.

Henrique L. Ennes, Moira I. Gresham, and Alexander F. Shaw

89(5), p. 511

A combination of analytical and numerical calculations is given for a two-body bound-state problem in quantum mechanics, closely related to that of the hydrogen atom and the deuterium nucleus. The interaction between particles is given by Yukawa forces, which generalizes that for the Coulomb force. Appropriate for advance undergraduate quantum mechanics classes.

Nathan Lima and Ricardo Karam

89(5), p. 521

Group velocity has been a key concept in attempts to reconcile the particle and wave approaches in quantum mechanics. Here, Lima and Karam explore two of these early struggles: Louis de Broglie's relativistic view of the wave accompanying a moving body and Erwin Schrödinger's derivation of the motion of a non-relativistic particle. The authors take us through the steps of de Broglie's and Schrödinger's developments, including the problems and inconsistencies they faced. Although both tried to formulate a consistent picture of the particle-wave duality, their developments were conceptually and technically very different. Actually, they only agreed on the assumption that particle velocity can be equaled to the wave group velocity. In addition to bringing some history of science in class, this paper can be used in undergraduate classes to show how two of the founding fathers of quantum mechanics battled, like the rest of us, to make sense of quantum reality.

B. Cameron Reed

89(5), p. 529

The finite rectangular potential well has been a staple of introductory quantum classes for decades. In recent years, it has enjoyed new interest as a theoretical tool to study the behavior of particles trapped within nanofabricated quantum corrals. The author presents a comprehensive, chronological review of the many techniques for finding the energy eigenvalues of the finite rectangular well, comparing their accuracy for a particular choice of well depth and width.

Ye-Jun Xu, Xiu-Chun Ding, Ji-Zhu Peng, and Shu-Dong Fang

89(5), p. 535

This brief paper presents a remarkably simple derivation of expressions of the harmonic oscillator position and momentum states | q ⟩ and | p ⟩, along with the energy eigenvalue (number) states | n ⟩ and the coherent states | z ⟩ in terms of operators acting on the vacuum state, appropriate for intermediate and advanced-level quantum mechanics.

Alain Perrier, Yvan Guilloit, Élodie Le Cren, and Yannick Dumeige

89(5), p. 535

The experimental study of photonic devices typically requires specialized fabrication facilities and complex optical instrumentation. In this paper, the authors use interleaved sections of 50 Ω and 75 Ω coaxial cables to mimic the behavior of single and multiple coupled optical resonators, allowing them to explore this fascinating field in the easily accessible radio frequency domain. Their measurements using simple instrumentation are in good agreement with theoretical predictions based on the transfer matrix method widely used in optics.

José P. Mestre and Jennifer L. Docktor

William J. Mullin, Reviewer

89(5), p. 546

A. Zee

Lawrence Weinstein, Reviewer

89(5), p. 547