Related papers: Upper-division student difficulties with the Dirac…
Students' difficulties in quantum mechanics may be the result of unproductive framing and not a fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantum mechanics…
Motivated by the problem of the dynamics of point-particles in high post-Newtonian (e.g. 3PN) approximations of general relativity, we consider a certain class of functions which are smooth except at some isolated points around which they…
This paper outlines a deceptively complex problem in classical mechanics which the paper names the "Falling Astronaut Problem," and it explores a method for teachers to implement this problem in an undergraduate classroom. The paper…
Fractional charges, and in particular the spectral asymmetry eta of certain Dirac operators, can appear in the central charge of supersymmetric field theories. This yields unexpected analyticity constraints on eta from which classic results…
Today, the 'hydrogen atom model' is known to play its role not only in teaching the basic elements of quantum mechanics but also for building up effective theories in atomic and molecular physics, quantum optics, plasma physics, or even in…
We discuss the clusters of resources that emerge when upper-division students write about electromagnetic fields in linear materials. The data analyzed for this paper comes from students' written tests in an upper-division electricity and…
Smooth, highly accurate analytical representations of Fermi-Dirac (FD) integral combinations important in free-energy density functional calculations are presented. Specific forms include those that occur in the local density approximation…
Traditional high-stakes summative assessments--timed, in-class exams accounting for a large percentage of the term's overall grade--have often received criticism from the educational community. Such assessments tend to prize a particular…
An equation, we call Dirac gamma-equation, is introduced with the help of the mathematical tools connected with the Clifford algebra. This equation can be considered as a generalization of the Dirac equation for the electron. Some features…
The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions. As model problem you may think…
The interactive textbook is created for English-speaking students whose study on Mathematical Calculus is based on modern programs of Ukrainian higher educational institutions. It includes personal tasks and samples on ``Integral Calculus…
Laboratory courses for upper-division undergraduates often involve sophisticated equipment, relatively small class sizes, and extended hands-on projects. These courses present distinct challenges and opportunities for the physics education…
The aim of the lectures is to introduce first-year Ph.D. students and research workers to the theory of the Dirac operator, spinor techniques, and their relevance for the theory of eigenvalues in Riemannian geometry. Topics: differential…
This paper aims to accelerate video stream processing, such as object detection and semantic segmentation, by leveraging the temporal redundancies that exist between video frames. Instead of propagating and warping features using motion…
In this paper, by making use of a certain family of fractional derivative operators in the complex domain, we introduce and investigate a new subclass $\mathcal{P}_{\tau,\mu}(k,\delta,\gamma)$ of analytic and univalent functions in the open…
Assessing student learning is a cornerstone of educational practice. Standardized assessments have played a significant role in the development of instruction, curricula, and educational spaces in college physics. However, the use of these…
Research has shown that both high school and university students' reasoning patterns regarding direct current resistive electric circuits often differ from the currently accepted explanations. At present, there are no standard diagnostic…
Previous research has shown that students often struggle to develop an understanding of linear and quadratic relationships. Covariational reasoning has been identified as a way to support this development. This study aims to investigate how…
Decades of research show that students learn more in classes that utilize active learning than they do in traditional, lecture-only classes. Active learning also reduces the achievement gaps that are often present between various…
An important goal of graduate physics core courses is to help students develop expertise in problem solving and improve their reasoning and meta-cognitive skills. We explore the conceptual difficulties of physics graduate students by…