Last month, I introduced a new feature: blurbs that would help readers/viewers decide quickly which articles are most likely to be most useful and appropriate for them. This is the second installment of this new feature.

## SCHRÖDINGER'S ORIGINAL STRUGGLES WITH A COMPLEX WAVE FUNCTION

*Ricardo Karam*

Schrödinger struggled against the apparently fundamental role of complex numbers in quantum mechanics. This historical description can be appreciated by anyone who has a basic familiarity with wave functions.

## THE PÉCLET NUMBER OF A CASINO: DIFFUSION AND CONVECTION IN A GAMBLING CONTEXT

*Cedric J. Gommes and Joe Tharakan*

By viewing convection as a large-scale averaging of interactions that are diffusive on small scales, a viewpoint is developed that can be applied to many phenomena including gambling. Students with some background in partial differential equations should be comfortable with the mathematical development.

## MAGNETOSTRICTION MEASUREMENTS WITH A LOW-COST MAGNETOSTRICTIVE CANTILEVER BEAM

*D. Laumann, P. Hayes, C. Enzingmüller, I. Parchmann, and E. Quandt*

A low-cost experiment is detailed in which magnetorestriction is inferred from cantilever bending. The article includes the theory of bending and is appropriate for an undergraduate laboratory project.

## EXPERIMENT ON PERCOLATION FOR INTRODUCTORY PHYSICS LABORATORIES—A CASE STUDY

*Daniel Dziob and Dagmara Sokołowska*

A laboratory experiment on the percolation of a water network was developed that meets the five goals of Introductory Physics Laboratories formulated by the American Association of Physics Teachers.

## ROLLING ALONG A SQUARE PATH: THE DYNAMICS OF BIASED BALLS

*Michael S. Wheatland, Rodney C. Cross, Andrew Ly, Michael Sacks, and Karl Smith*

A truncated billiard ball that rolls without slipping exhibits interesting and unexpected dynamics. The center of mass can move in circular, square, or triangular paths depending on the initial conditions. Both the analytic and numerical aspects are appropriate for mechanics at the advanced undergraduate level.

## FORM OF SPINNING LIQUIDS IN DIVERSE GEOMETRIES

*Paul Menker and Andrzej Herczyński*

The steady-state rotation of water in various containers is studied both analytically and experimentally. Using relatively simple algebra, one can calculate the critical angular speed for a rotating liquid to change its surface topology, and that agrees quite well with the experimental value.

## COMPUTER SIMULATION OF MERMIN'S QUANTUM DEVICE

*Robert Ross*

This article is very explicitly designed for students early in their study of quantum mechanics, typically in modern physics courses. By using a simple computer simulation of a quantum information scenario, it introduces an essential part of what should be taught, without mathematics that the students do not yet have.

## A FULLY MANIPULABLE DAMPED DRIVEN HARMONIC OSCILLATOR USING OPTICAL LEVITATION

*Javier Tello Marmolejo, Oscar Isaksson, Remigio Cabrera-Trujillo, Niels C. Giesselmann, and Dag Hanstorp*

In this Instructional Labs & Demos paper, optical levitation and manipulation of an oil drop give a laboratory setting for connecting to the theoretical damping and driving of a simple harmonic oscillator. While the theory is at the level of university physics, the laboratory work may be useful for graduate instruction.

## A NOTE ON A STRAIGHT GRAVITY TUNNEL THROUGH A ROTATING BODY

*Aleksander Simonič*

The motion is studied of a frictionless “train” driven by gravity along a straight tunnel in a rotating spherically symmetric model of the Earth. Conditions and time for traversability are calculated. The content is mostly at the level of intermediate undergraduate mechanics.

## THE HELLMANN-FEYNMAN THEOREM AT FINITE TEMPERATURE

*Marina Pons, Bruno Juliá-Díaz, Artur Polls, Arnau Rios, and Isaac Vidaña*

A simple proof is given of the Hellmann-Feynman theorem, for simplified calculation of some expectation values, for a thermal distribution of states, along with three examples of applications. Two of these are appropriate for an undergraduate quantum course, while the third requires an advanced graduate course background.