Related papers: Upper-division student difficulties with the Dirac…
Deep Reinforcement Learning (DRL) is emerging as a promising approach to generate adaptive behaviors for robotic platforms. However, a major drawback of using DRL is the data-hungry training regime that requires millions of trial and error…
By expanding the Dirac delta function in terms of the eigenfunctions of the corresponding Sturm-Liouville problem, we construct some new (oscillating) integral transforms. These transforms are then used to solve various finance, physics,…
In upper-division undergraduate physics courses, it is desirable to give numerical problem-solving exercises integrated naturally into weekly problem sets. I explain a method for doing this that makes use of the built-in class structure of…
In this work, we introduce the new class of functions which can use to solve the nonlinear/linear multi-dimensional differential equations. Based on these functions, a numerical method is provided which is called the Developed Lagrange…
Grading can shape students' learning and encourage use of effective problem solving practices. Teaching assistants (TAs) are often responsible for grading student solutions and providing feedback, thus, their perceptions of grading may…
Some years ago, one of the authors~(MM) revived a concept to which he gave the name of single-particle Dirac oscillator, while another~(CQ) showed that it corresponds to a realization of supersymmetric quantum mechanics. The Dirac…
We introduced some contact potentials that can be written as a linear combination of the Dirac delta and its first derivative, the $\delta$-$\delta'$ interaction. After a simple general presentation in one dimension, we briefly discuss a…
In this article we consider regularizations of the Dirac delta distribution with applications to prototypical elliptic and hyperbolic partial differential equations (PDEs). We study the convergence of a sequence of distributions…
A close look at students' written work on examinations offers a wealth of information about their performance, their knowledge of the subject, their strengths, weaknesses and misconceptions, and their overall level of mathematical skills…
We study theoretically the level shift of the Dirac oscillator perturbed by any sharply peaked potential approaching a surface delta potential. A Green function method is used to obtain closed expressions for all partial waves and parities.
We are interested in better understanding ways that students collaborate to solve conceptual physics problems in the context of spherical unit vectors in upper-level E&M, especially problems that have been shown to be difficult for students…
The Colorado Upper-Division Electrostatics (CUE) Diagnostic is an exam developed as part of the curriculum reform at the University of Colorado, Boulder (CU). It was designed to assess conceptual learning within upper-division electricity…
From a department being resistant to change to students not buying into the new computational activities, the challenges that are faced with integrating computation into the physics undergraduate curriculum are varied. The Partnership for…
We show that the Dirac factorization method can be successfully employed to treat problems involving operators raised to a fractional power. The technique we adopt is based on an extension of the Pauli matrices and the properties of the…
This paper shows the Fermi-Dirac Integrals expressed in terms of Riemann and Hurwitz Zeta functions. This is done by defining an auxiliar function that permits rewrite the Fermi-Dirac integral in terms of simpler and known integrals…
The core concept of quantum simulation is the mapping of an inaccessible quantum system onto a controllable one by identifying analogous dynamics. We map the Dirac equation of relativistic quantum mechanics in 3+1 dimensions onto a…
The use of Data Retrieval Tests (DRTs), as an alternative to physics laboratory notebook marking, is discussed. The implementation of a Moodle-based, on-line DRT for 1st year physics students is described. The advantages of using such a…
Computation is becoming an increasingly important part of physics education. However, there are currently few theories of learning that can be used to help explain and predict the unique challenges and affordances associated with…
How students use mathematics in their physics classes has been studied extensively in the physics education literature. In addition to specific mathematical methods in specific physics contexts, possible effects of more general "cultural"…
Helping students become proficient problem-solvers is one of the primary goals of physics courses. In part 1 of this article, we summarized the vast research on problem-solving relevant for physics instruction, and here we discuss a…