Related papers: Student Difficulties with the Dirac Delta Function
Whereas the Dirac delta function introduced by P. A. M. Dirac in 1930 in his famous quantum mechanics text has been well studied, a not famous formula related to the delta function using the Heaviside step function in a single-variable…
Teaching assistants (TAs) are often responsible for grading student solutions. Since grading communicates instructors' expectations, TAs' grading decisions play a crucial role in forming students' approaches to problem solving (PS) in…
Possibilities for defining the radial derivative of the delta distribution $\delta(\underline{x})$ in the setting of spherical coordinates are explored. This leads to the introduction of a new class of continuous linear functionals similar…
The problem of bound states in delta potentials is revisited by means of Fourier transform approach. The problem in a simple delta potential sums up to solve an algebraic equation of degree one for the Fourier transform of the eigenfunction…
We investigate introductory physics students' difficulties in translating between mathematical and graphical representations and the effect of scaffolding on students' performance. We gave a typical problem that can be solved using Gauss's…
In most introductory courses on electrodynamics, one is taught the electric charge is quantised but no theoretical explanation related to this law of nature is offered. Such an explanation is postponed to graduate courses on…
We demonstrate how to make the coordinate transformation or change of variables from Cartesian coordinates to curvilinear coordinates by making use of a convolution of a function with Dirac delta functions whose arguments are determined by…
If $T$ is a (densely defined) self-adjoint operator acting on a complex Hilbert space $\mathcal{H}$ and $I$ stands for the identity operator, we introduce the delta function operator $\lambda \mapsto \delta \left(\lambda I-T\right) $ at…
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.
One hallmark of expertise in physics is the ability to translate between different representations of knowledge and use the representations that make the problem-solving process easier. In quantum mechanics, students learn about several…
Computational physics is a key part of what it means to do physics in the twenty-first century. However, upper division computational physics remains a largely understudied area. We set out to understand the experiences of students in an…
Science is facing a reproducibility crisis. Previous work has proposed incorporating data analysis replications into classrooms as a potential solution. However, despite the potential benefits, it is unclear whether this approach is…
"Self-diagnosis tasks" aim at fostering diagnostic behavior by explicitly requiring students to present diagnosis as part of the activity of reviewing their problem solutions. We have been investigating the extent to which introductory…
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…
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 use the Survey of Thermodynamic Processes and First and Second Laws-Long (STPFaSL-Long), a research-based survey instrument with 78 items at the level of introductory physics, to investigate introductory and advanced students'…
Development of conceptual multiple-choice tests related to a particular physics topic is important for designing research-based learning tools to reduce the difficulties. We explore the difficulties that the advanced undergraduate and…
During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on…
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a problem into a representation that is easier to exploit for solving it. One major focus while helping introductory physics students learn effective…
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…