Issues

Editor's Note: This paper is the text of a plenary talk given by the author at the AAPT Summer 2024 meeting when she accepted the David Halliday and Robert Resnick Award for Excellence in Undergraduate Physics Teaching.

Editor's Note: This paper is the text of a plenary talk given by the author at the AAPT Summer 2024 meeting when she accepted the J.D. Jackson Award for Excellence in Graduate Physics Education.

Editor's Note: This article presents an intuitive approach to infinite cross sections by way of the “scattering shadow” of a repulsive potential. The authors apply classical scattering theory to repulsive power-law and Yukawa potentials, present numerical methods for calculating the envelope of trajectories that define the shadow, and derive analytic expressions for its asymptotic behavior. Scattering shadows clearly illustrate the physical origin of infinite cross sections. As such, the approach complements traditional analyses of scattering cross sections based on the impact parameter or differential cross section, common in texts and courses on classical scattering and quantum mechanics.

Editor's Note: The authors present a clever derivation of the static electric and magnetic field energy densities for capacitors and inductors of any shape. The derivations generalize the simple and often discussed cases of infinite parallel plate capacitors and infinitely long solenoids while requiring only a conceptual understanding of integral vector calculus. The discussion is suitable for introductory physics courses and will be of interest for teachers seeking new ways to introduce the challenging concept of field energy density.

Editor's Note: For many reasons, magnetism is extremely challenging for the introductory physics student. Magnetic forces are non-intuitive and jarringly different than electric forces. Problems involving magnetism traditionally require three-dimensional reasoning, cross products, and right-hand rules. It is natural to wonder whether new teaching approaches can help students learn such a difficult subject. Building on earlier work in rotational physics, this article explores a non-traditional pedagogical approach where bivectors (represented by oriented tiles) are used to teach magnetism. This fresh perspective may help students avoid pitfalls associated with the traditional approach, while also preparing them for more advanced discussions of relativistic electromagnetism.

Editor's Note: The question asked in this paper's title falls in the category of “Why didn't I think to ask that?” It is answered in just the way that you will want to answer it in a class: first with an experimental demonstration that larger objects result in smaller and dimmer Poisson spots, followed by a simple calculation, and then completed with a more careful calculation that is still not too hard to present in class. This seems to be appropriate for an introductory or intermediate optics course.

Editor's Note: The reflectionless potential, also called the Pöschl–Teller potential, is one of the less-often discussed quantum potentials with known analytical solutions. The system has many interesting properties, including the fact that it allows both bound and scattering states and that the potential well never reflects incident particles. The authors here present new ways to think about the somewhat counter-intuitive completeness of the set of bound and scattering states of the system.

Editor's Note: Could a laser rangefinder give constant readings even though the distance between two objects is changing? Will two observers always agree about whether they are moving toward each other or away from each other? This paper analyzes accelerating observers within the frameworks of Newtonian physics and special relativity to reveal how classical intuition about such questions can lead one astray. The author then demonstrates how accelerated motion in special relativity can provide insight into gravitational redshifts and event horizons in general relativity. Only algebra and calculus are used in the analysis, making these intriguing “paradoxes” accessible to students in modern physics or a first course in relativity.

Editor's Note: The finite spacetime manifold in which outgoing waves reach infinity in a finite spacetime interval was introduced in the 1960s by Roger Penrose. It plays an important role in the analysis of gravitational waves. In this work the author shows how to construct a temporal foliation using spacelike slices with hyperbolic geometry in compactified Minkowski space. Instructors in special relativity will be able to make these ideas accessible to their students, including an application to massless fields in flat spacetime.

Editor's Note: Solving the Schrödinger equation to find energies and wave functions is hard, so in the classroom, we're normally limited to a few potentials that have analytical solutions. This paper turns the problem around: what if you start with a wave function and ask what potential this solves? Use this idea to generate some new problems for your undergraduate or graduate quantum mechanics course.

Editor's Note: This brief note shows how symmetry arguments can be used to find the B-field of an infinite solenoid with a non-circular cross section and includes a review of how the pseudovector B behaves on reflection.

Editor's Note: A straightforward approximate algebraic procedure for introducing locally flat coordinates in a Schwarzschild spacetime is undertaken in this Comment on the recent leading order differential approach elucidated by Steven Balbus in the June 2024 issue. It is very likely that instructors even in special relativity could employ this technique and thereby obtain the correct deflection angle for light in an accelerated frame of reference.