August 2026
Volume 94, Issue No. 8
Yujun Shi; Xiaoting Feng
Am. J. Phys. 94, 631–639 (2026) https://doi.org/10.1119/5.0255710
We revisit Koehler's experiment, a clever modification of Rüchardt's experiment designed to measure the ratio of specific heats of gas. However, the lengthy and dense analysis shared by Koehler in his 1950 paper may pose challenges to readers due to the complexity of the calculations. Following Koehler's approximation for pressure changes, we explicitly present the model equations as piecewise linear differential systems and qualitatively analyze the periodic solutions from a geometric perspective. This concise and transparent approach addresses a fundamental question about Koehler's experiment: why is the oscillation frequency nearly equal to the Rüchardt frequency? Our analysis avoids intricate calculations and should help educators introduce Koehler's experiment in general physics laboratory classes.
EDITORIAL
In this issue: August 2026 by Geraldine L. Cochran; John Essick; Harvey Gould; Claire A. Marrache-Kikuchi; Beth Parks; Daniel Schumayer; Todd Springer; Jan Tobochnik. DOI: 10.1119/5.0349316
LETTERS TO THE EDITOR
Johannes Vermeer and The Guitar Player: Observations on the vibrating guitar string's edge by Geoffrey D. Schott. DOI: 10.1119/5.0338541
An improved version of the “extraordinary tabletop speed of light apparatus” by G. Pegna; G. Malloci. DOI: 10.1119/5.0347633
Editor's Note: An improved version of the previously published tabletop speed of light apparatus is presented, in which the amplitude modulation frequency is more than doubled, enabling a reduction in the overall size of the apparatus, while improving the precision of the measured value for c. Detailed construction instructions are provided in supplementary material.
Early use of dimensional analysis in quantum theory by Kirk T. McDonald. DOI: 10.1119/5.0337153.
RESOURCE LETTERS
Resource Letter QIE-1: Research in quantum information education by Josephine C. Meyer; Simon Goorney; Tunde Kushimo; Zeki C. Seskir. DOI: 10.1119/5.0306510
Editor's Note: The United Nations designation of 2025 as the International Year of Quantum Science and Technology reflects the growing global investment in quantum information science and engineering (QISE) and the rising need for education in this field at all levels. This Resource Letter surveys the literature supporting QISE education, with resources spanning high school (secondary school) through graduate level instruction. The majority of the cited works do not assume familiarity with QISE content beyond a standard middle-division undergraduate course. This list of resources is not intended to be exhaustive or definitive; rather, it offers a curated entry point into the robust and rapidly growing body of literature that has developed in recent years to meet the expanding demand for QISE education.
PAPERS
Problem solving in physics classes: Navigating fast and slow thinking by Alexander Godunov. DOI: 10.1119/5.0269803
Editor's Note: Inspired by Daniel Kahneman's dual-process theory, the author developed and tested a six-step problem-solving framework for students in introductory courses. Initial testing showed that students who were required to use this framework in their homework scored significantly higher on the final exam compared to students who were simply exposed to it in lecture. Give it a try in your courses!
QISCIT: A concept inventory assessment for quantum information science by Kelley Durkin; Manshuo Lin; Michael H. Kolodrubetz; Ryan P. McMahan. DOI: 10.1119/5.0287731
Editor's Note: This paper describes the development of the Quantum Information Science Concept Introductory Test. This 31-item assessment includes concepts of quantum states, quantum measurement, qubits, entanglement, coherence, quantum gates, and quantum teleportation. It is designed to provide a useful assessment at the high school or university level.
The inverse velocity force and automotive physics by Chris L. Lin. DOI: 10.1119/5.0278714
Editor's Note: Do you think of your car's transmission as a source of “inverse velocity force”? This article shows why you should! Along with gaining a deeper understanding of transmissions, readers will see how to apply mechanics to cars with both electric and internal combustion engines. Instructors looking for new ways to connect classroom physics to the “real world” will enjoy this paper.
A rigorous derivation of the ideal gas law from energy constraints by Daniele Battesimo Provenzano. DOI: 10.1119/5.0323616
Editor's Note: The article follows an unusual path in thermodynamics. It offers a purely thermodynamic derivation of the ideal gas law that bypasses both empirical postulates and kinetic theory and shows how the equation of state emerges from simple energy-based constraints. Exploiting the symmetry of thermodynamic potentials deepens the conceptual understanding of why the ideal gas law is mathematically equivalent to specific energy independences rather than being an external assumption.
Revisiting Koehler's experiment of measuring the ratio of the specific heats of air by self-sustained oscillations by Yujun Shi; Xiaoting Feng. DOI: 10.1119/5.0255710
Editor's Note: Koehler's experiment is an improvement of Rüchardt's experiment to measure the heat capacity ratio (Laplace coefficient), in which a ball seals a vertical tube connected to a container full of air. If gas is supplied to the container and the air is allowed to escape through a hole in the vertical tube whenever the ball rises above it, the ball may exhibit self-sustained oscillations. This motion is explored here, from both experimental and dynamical systems points of view. Koehler's experiment is relevant for introductory thermodynamics courses, while the full theoretical and computational analysis could be left for advanced thermodynamics or computational physics classes.
ADVANCED TOPICS
Generalized vibration curves for apodization and super-resolution in far-field diffraction by Lowell T. Wood. DOI: 10.1119/5.0300919
Editor's Note: This work uses generalized vibration curves to present a unified geometric interpretation of apodization and the resulting diffraction structures. It is appropriate for use in optics courses beyond the introductory level.
Kapitza's pendulum as a classical prelude to Floquet–Magnus theory by Johannes K. Krondorfer; Maria Kainz; Matthias Diez; Andreas W. Hauser. DOI: 10.1119/5.0295025
Editor's Note: Driven systems, that is systems submitted to an external forcing, play an important role in modern physics since time-dependent driving can generate entirely new effective behaviors and even stabilize otherwise unstable configurations. One of the simplest examples is Kapitza's pendulum, where rapid periodic driving stabilizes the inverted, upward position of the pendulum. This article takes this problem as a pretext to introduce Floquet theory and Magnus expansion, which are commonly employed to study driven systems. Floquet theory describes periodically driven systems by separating the dynamics into an effective long-time evolution governed by a Hamiltonian and a periodic micromotion capturing the oscillations at short timescales. This article therefore provides an accessible introduction to the physics of driven systems and the corresponding theoretical methods, useful at the advanced undergraduate and graduate levels.
Operator-based derivation of symmetric molecular top wavefunctions by J. Stocker; J. K. Freericks. DOI: 10.1119/5.0297905
Editor's Note: Introductory quantum mechanics courses often cover the rigid rotor (two atoms separated by a fixed distance R) as a model of diatomic molecules. The rotational energy spectrum can be found by solving the Schrödinger equation, and the resulting eigenfunctions are the familiar spherical harmonics. Students interested in modeling more complex molecules with reduced symmetry (for example, a water molecule) will need to become familiar with “symmetric top” wavefunctions, which take the place of the spherical harmonics. In this article, the authors derive these wavefunctions using operator algebra, and provide applications to the physics of water molecules. The article will be of interest to instructors who may want to make more contact between quantum mechanics courses and physical chemistry, as well as to readers seeking inspiration for student projects in this direction.
Tuning interatomic forces with magnetic fields: Feshbach resonances in lithium-6 by Ettore Vitali; Gino Edward Gamboni. DOI: 10.1119/5.0287600
Editor's Note: The Feshbach resonance strongly affects the interactions between atoms in ultracold atomic gases via an applied magnetic field, tuning from a weakly interacting gas to a strongly correlated many-body system. This paper explains the resonance in 6Li at a level appropriate for students whose undergraduate quantum mechanics course has already discussed scattering theory.
Bloch's theorem: An operator-based derivation by Celal Sirin. DOI: 10.1119/5.0310014
Editor's Note: When Bloch's theorem is presented in solid-state physics courses, normally the proofs make use of the formalism of periodic structures that has already been derived in the course. This paper presents an alternative demonstration, which uses the position and momentum translation operators and avoids the use of Schrödinger's differential equation in position representation. Quantum mechanics instructors who emphasize an operator approach will appreciate this alternative derivation.
COMPUTATIONAL PHYSICS
A time-domain approach to band formation in periodic media by Nishant Kashyap, Amit Tanwar, Pragati Ashdhir, Vivek T. Ramamoorthy. DOI: 10.1119/5.0345054
Editor's Note: This paper explains how band gaps originate in solids by numerically solving the real-space wave dynamics of a simple periodic structure. In addition, the authors discuss the connection between the usual approach using Bloch's theorem for infinite systems and the numerical approach for finite systems.
Tracking the spread of chaos in the swinging Atwood machine by Nick Tufillaro. DOI: 10.1119/5.0344894
Editor's note: This paper analyzes the swinging Atwood machine, which can exhibit chaotic behavior, using computational tools which were originally developed for astronomical simulations. The paper is accessible to undergraduates.
INSTRUCTIONAL LABORATORIES AND DEMONSTRATIONS
An advanced undergraduate lab on laser noise detection analyzed with a quantum formalism by Haoran Liu; Zhou Fang; Qing Xu; Sujing Cao; Zeliang Wu; Yuan Wu; Jinxian Guo; L. Q. Chen. DOI: 10.1119/5.0298492
Editor's Note: Characterizing and understanding noise is fundamental to experiments, and the growing importance of quantum measurement increases the importance of understanding the distinct characteristics of quantum and classical laser noise. This paper describes an undergraduate laboratory exercise in which students learn to identify noise sources by observing how laser noise varies with frequency and power.
The asymmetric rotating saddle potential as a mechanical analog to the RF Paul trap by Aidan Carey; Laurel Barnett; Robert Hart; Anna Klales; Ali Kurmus; Louis Deslauriers. DOI: 10.1119/5.0274638
Editor's Note: This paper examines the impact of asymmetry in rotating saddle potentials, a mechanical analog to RF Paul traps used for confining charged particles. The authors demonstrate that even minor asymmetries, such as those from manufacturing imperfections, can significantly alter particle trajectories and stability. This paper is appropriate for advanced E&M classes for educators who wish to connect with topics such as quantum mechanics or quantum technologies. It is also an interesting example of dynamical system and, as such, could be a possible topic for a student project in computing.
Demonstrating dynamic stability with rotating saddles and liquid nitrogen droplets: A classroom analog to the RF Paul trap by Laurel Barnett; Aidan Carey; Robert Hart; Daniel Davis; Anna Klales; Louis Deslauriers. DOI: 10.1119/5.0279658
Editor's Note: This paper describes a classroom demonstration in which liquid nitrogen droplets are used as test particles on a rotating saddle surface to show dynamical confinement, similar to the ponderomotive force experienced by charged particles in a Paul trap. After providing the theoretical background needed to understand the experimental setup, the dynamic stability of liquid nitrogen droplets is shown to be significantly better than that of ball bearings that have been traditionally used in such demonstrations. The authors offer practical guidance on assembling and implementing this enhanced demonstration.
Additional Resources
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