A Solvable Model for Decoupling of Interacting Clusters

We consider M clusters of interacting particles, whose in-group interactions are arbitrary, and inter-group interactions are approximated by oscillator potentials. We show that there are masses and frequencies that decouple the in-group and inter-group degrees of freedom, which reduces the initial problem to M independent problems that describe each of the relative in-group systems. The dynamics of the M center-of-mass coordinates is described by the analytically solvable problem of M coupled harmonic oscillators. This paper derives and discusses these decoupling conditions. Furthermore, to illustrate our findings, we consider a charged impurity interacting with a ring of ions. We argue that the impurity can be used to probe the center-of-mass dynamics of the ions.Comment: Version accepted for publication in EP

An Item Response Curves Analysis of the Force Concept Inventory

Several years ago, we introduced the idea of item response curves (IRC), a simplistic form of item response theory (IRT), to the physics education research community as a way to examine item performance on diagnostic instruments such as the Force Concept Inventory (FCI). We noted that a full-blown analysis using IRT would be a next logical step, which several authors have since taken. In this paper, we show that our simple approach not only yields similar conclusions in the analysis of the performance of items on the FCI to the more sophisticated and complex IRT analyses but also permits additional insights by characterizing both the correct and incorrect answer choices. Our IRC approach can be applied to a variety of multiple-choice assessments but, as applied to a carefully designed instrument such as the FCI, allows us to probe student understanding as a function of ability level through an examination of each answer choice. We imagine that physics teachers could use IRC analysis to identify prominent misconceptions and tailor their instruction to combat those misconceptions, fulfilling the FCI authors\u27 original intentions for its use. Furthermore, the IRC analysis can assist test designers to improve their assessments by identifying nonfunctioning distractors that can be replaced with distractors attractive to students at various ability levels

Poincare Semigroup Symmetry as an Emergent Property of Unstable Systems

The notion that elementary systems correspond to irreducible representations of the Poincare group is the starting point for this paper, which then goes on to discuss how a semigroup for the time evolution of unstable states and resonances could emerge from the underlying Poincare symmetry. Important tools in this analysis are the Clebsch-Gordan coefficients for the Poincare group.Comment: 17 pages, 1 figur

On representing resonances and decaying states

textPhysic

Point–Counterpoint: Can Anything Be Learned from Surveys on the Interpretations of Quantum Mechanics?

In what follows, Matt Leifer and Nathan Harshman present opposing views on the value of surveys on foundational attitudes towards quantum mechanics. Three such surveys were recently published and their results are summarized in Table 1. Matt takes the `point,’ arguing that such surveys are not useful, while Nathan takes the `counterpoint.’ A complete set of references for both is given at the end

Testing the test: item response curves and test quality

We present a simple technique for evaluating multiple-choice questions and their answers beyond the usual measures of difficulty and the effectiveness of distractors. The technique involves the construction and qualitative consideration of item response curves and is based on item response theory from the field of education measurement. To demonstrate the technique, we apply item response curve analysis to three questions from the Force Concept Inventory. Item response curve analysis allows us to characterize qualitatively whether these questions are efficient, where efficient is defined in terms of the construction, performance, and discrimination of a question and its answer choices. This technique can be used to develop future multiple-choice examination questions and a better understanding of results from existing diagnostic instruments