Related papers: Student difficulties with representations of quant…
The discrimination of quantum operations has long been an intriguing challenge, with theoretical research significantly advancing our understanding of the quantum features in discriminating quantum objects. This challenge is closely related…
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…
Unifying quantum theory and gravity remains a fundamental challenge in physics. While most existing literature focuses on the ultraviolet (UV) modifications of quantum theory due to gravity, this work shows that generic infrared (IR)…
This book is an attempt to help students transform all of the concepts of quantum mechanics into concrete computer representations, which can be constructed, evaluated, analyzed, and hopefully understood at a deeper level than what is…
The problem of simulating through quantum walks Dirac fermions in arbitrary curved space-times and coordinates is revisited, taking (1 + 1)D space-times as an example. A new shift or translation operator on the grid is introduced, to take…
In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
Identifying and understanding student difficulties with physics content in a wide variety of topical areas is an active research area within the PER community. In many cases, physics topics appear multiple times in different contexts across…
A study of fundamental geometrical interactions shows that the Dirac electron can be represented as a conformal wave. A Riemannian space is used, having coordinates that transform locally as spinors. The wave function becomes a gradient.…
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…
Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and…
This paper examines the Foldy-Wouthuysen and Feynman-Gell-Mann representations of the Dirac equation. The analysis is conducted for electrons and positrons interacting with electromagnetic fields. Versions of quantum electrodynamics are…
Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal solutions of the Dirac equation.
Highly successful students, as measured by grades and by scores on the Force Concept Inventory, still struggle with fundamental concepts in mathematics and physics. These difficulties, which turn physics into parrot learning and include…
Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector…
We demonstrate that the Dirac representation theory can be effectively adjusted and applied to signal theory. The main emphasis is on orthogonality as the principal physical requirement. The particular role of the identity and projection…
A generalized algebra of quantum observables, depending on extra dimensional constants, is considered. Some limiting forms of the algebra are investigated and their possible applications to the descriptions of interactions of fundamental…
These notes provide an introduction to standard topics on quantum computation and communication for those who already have a basic knowledge of quantum mechanics. The main target audience are professional physicists as well as advanced…
Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…
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…