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Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think…
High school science classrooms across the United States are answering calls to make computation a part of science learning. The problem is that there is little known about the barriers to learning that computation might bring to a science…
The use of validated conceptual assessments alongside more standard course exams has become standard practice for the introductory courses in many physics departments. These assessments provide a more standard measure of certain learning…
Mathematics is the language of science. Fluent and productive use of mathematics requires one to understand the meaning embodied in mathematical symbols, operators, syntax, etc., which can be a difficult task. For instance, in algebraic…
Question Answering (QA) has proved to be an arduous challenge in the area of natural language processing (NLP) and artificial intelligence (AI). Many attempts have been made to develop complete solutions for QA as well as improving…
To explore the possibilities of a near-term intermediate-scale quantum algorithm and long-term fault-tolerant quantum computing, a fast and versatile quantum circuit simulator is needed. Here, we introduce Qulacs, a fast simulator for…
In this paper we consider the problem of the occurrence of spurious modes when computing the eigenvalues of Dirac operators, with the motivation to describe relativistic electrons in an atom or a molecule. We present recent mathematical…
Introductory undergraduate courses in classical physics stress a perspective that can be characterized as realist; from this perspective, all physical properties of a classical system can be simultaneously specified and thus determined at…
We discuss how a class of difficult kinematic problems can play an important role in an introductory course in stimulating students' reasoning on more complex physical situations. The problems presented here have an elementary analysis once…
In 1926, Dirac stated that quantum mechanics can be obtained from classical theory through a change in the only rule. In his view, classical mechanics is formulated through commutative quantities (c-numbers) while quantum mechanics requires…
This article reports on a student summer project performed in 2006 at the University of Frankfurt. It is addressed to undergraduate students familiar with the basic principles of relativistic quantum mechanics and general relativity. The…
Since its inception at the beginning of the twentieth century, quantum mechanics has challenged our conceptions of how the universe ought to work; however, the equations of quantum mechanics can be too computationally difficult to solve…
We study the existence of quantum resonances of the three-dimensional semiclassical Dirac operator perturbed by smooth, bounded and real-valued scalar potentials $V$ decaying like $\langle x \rangle ^{-\d}$ at infinity for some $\d >0$. By…
In this case study, we investigated the effectiveness of peer interaction on responses to in-class clicker questions in an upper-level quantum mechanics course. We analyzed student performance on clicker questions answered individually and…
This paper presents a case-study assessing and analyzing student engagement with and responses to binary, descriptive, and computational questions testing the concepts underlying resistor networks (series and parallel combinations). The…
Exact procedures that follow Dirac's constraint quantization of gauge theories are usually technically involved and often difficult to implement in practice. We overview an "effective" scheme for obtaining the leading order semiclassical…
Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of…
Students are taught several models of conductivity, both at the introductory and the advanced level. From early macroscopic models of current flow in circuits, through the discussion of microscopic particle descriptions of electrons flowing…
It is shown that the squared operation of the Dirac equation which is widely applied may create new solutions and moreover may change the inner nature of original equation. Some illustrating examples are considered as well.
We describe the development of a junior-senior level course for Physics majors designed to teach Mathematica skills in support of their undergraduate coursework, but also to introduce students to modern research level results. Standard…