Related papers: Investigating Student Difficulties with Dirac Nota…
In this research, we investigate the quantum and classical phase transitions of the Dirac particles in a homogeneously magnetized curved rotating 2+1 dimensional spacetime. We consider the intricate relationship between geometry and quantum…
The fundamental principles of quantum mechanics are considered to be hard for understanding by unprepared listeners, many attempts of its popularization turned out to be either difficult to grasp or incorrect. We propose quantum…
Understanding instructor attitudes and approaches to teaching quantum mechanics can be helpful in developing research-based learning tools. Here we discuss the findings from a survey in which 13 instructors reflected on issues related to…
Since the particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle…
Undergraduate students of physics in Tibet have great difficulty learning quantum mechanics (QM). We attempt to use PER-based methods to help Tibetan students learn QM. In this preliminary study, we incorporate Mathematica in a QM course at…
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…
We give an explicit operator realization of Dirac quantization of free particle motion on a surface of codimension 1. It is shown that the Dirac recipe is ambiguous and a natural way of fixing this problem is proposed. We also introduce 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…
Quantum information is an emerging field which has attracted a lot of attention in the last fifteen years or so. It is a broad subject which covers from the most applied questions (e.g., how to build quantum computers or secure…
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…
Explication and reflection on expert vs. novice considerations within the problem-solving process characterize a cognitive apprenticeship approach for the development of expert-like problem solving practices. In the context of grading, a…
We discuss an investigation of student difficulties with the corrections to the energy spectrum of the hydrogen atom for the intermediate field Zeeman effect using the degenerate perturbation theory. The investigation was carried out in…
Quantum optimization, a key application of quantum computing, has traditionally been stymied by the linearly increasing complexity of gradient calculations with an increasing number of parameters. This work bridges the gap between Koopman…
These brief lecture notes are intended mainly for undergraduate students in engineering or physics or mathematics who have met or will soon be meeting the Dirac delta function and some other objects related to it. These students might have…
A common learning goal for modern physics instructors is for students to recognize a difference between the experimental uncertainty of classical physics and the fundamental uncertainty of quantum mechanics. Our prior work has shown that…
Comparison of answers offered by a computer algebra system (CAS) with answers derived by a student without a CAS is relevant, for instance, in the context of computer-aided assessment (CAA). The issues of identity, equivalence and…
The Dirac procedure for dealing with constraints is applied to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first class constraints that arise and the resulting Dirac brackets…
In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred and…
The Dirac equation, usually obtained by `quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic…
An efficient quantum algorithm for the many-body three-dimensional Dirac equation is presented. Its computational complexity is dominantly linear in the number of qubits used to spatially resolve the 4-spinor wave function.