Chaos is investigated in the swinging Atwood machine as the mass ratio mu decreases from the integrable motion at mu=3 to mostly chaotic dynamics at mu=2.7. The spread of chaos is characterized by combining a stability index with a Poincar & eacute; surface of section. An effective computational solution requires a consideration of numerical overflow issues. Once these are resolved, the computation shows that the spread of chaos, in this parameter regime, is associated with a hyperbolic periodic loop orbit. The example illustrates how to incorporate computational physics-such as the regularization of a singularity-into the undergraduate curriculum.
The symmetric top wavefunctions are important in the study of rotational transitions of rigid body-rotor molecules. Using an explicit construction of the position-space state (determined from the Euler angles) and the definite angular momentum states (determined from the total angular momentum and the projections in the lab and body-fixed frames), we provide an operator-based derivation of these wavefunctions that just uses abstract states and operators without the need to work in position space. This is a representation-independent way to construct the wavefunction, providing an alternative to more common differential equation approaches. As an example application, we illustrate how they can be used to calculate the linewidth of the pure rotational transitions in the asymmetric top water molecule.
We revisit Koehler's experiment, a clever modification of R & uuml;chardt'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 R & uuml;chardt frequency? Our analysis avoids intricate calculations and should help educators introduce Koehler's experiment in general physics laboratory classes.
Both quantum and classical noise are fundamental features of laser beams. This work introduces a quantum optics model to distinguish the two types of noise in a Michelson interferometer experiment for undergraduate education. By measuring photon flux noise in an interferometer, this lab enables undergraduates to observe quantum fluctuations in real data, distinguish quantum noise from classical noise, and develop hands-on skills in optical alignment and quantum measurement. By turning abstract quantum concepts into tangible experiences, it provides foundational training for emerging quantum technologies.
This paper examines the cognitive foundations of problem solving in introductory physics, drawing on Daniel Kahneman's dual-process theory and research on judgment and decision making. Students often struggle with problem analysis, mathematical reasoning, and cognitive biases. To address these challenges, the paper proposes a six-step problem-solving framework grounded in dual-process principles and integrates it with structured problem-solving journals. The framework and journals were implemented in university physics courses, where students were required to make their reasoning explicit in written homework. In a controlled classroom study, students who consistently applied the six-step structure in written journals scored 24% higher on average on the final exam than peers who completed only online homework. These findings illustrate how slowing down intuitive responses and examining assumptions allows students to engage more fully in analytical problem solving.
