Related papers: Teaching Rotational Physics with Bivectors
The conformability of angular observales (angular momentum and azimuthal angle) with the mathematical rules of quantum mechanics is a question which still rouses debates. It is valued negatively within the existing approaches which are…
The Dirac belt trick is often employed in physics classrooms to show that a $2\pi$ rotation is not topologically equivalent to the absence of rotation whereas a $4\pi$ rotation is, mirroring a key property of quaternions and their…
In the Special Theory of Relativity space and time intervals are different in different frames of reference. As a consequence, the quantity 'velocity' of classical mechanics splits into different quantities in Special Relativity, coordinate…
The pendulum, in the presence of linear dissipation and a constant torque, is a non-integrable, nonlinear differential equation. In this paper, using the idea of rotated vector fields, derives the relation between the applied force $\beta$…
Machine learning of scalar molecular properties such as potential energy has enabled widespread applications. However, there are relatively few machine learning models targeting directional properties, including permanent and transition…
We give an explicit and general description of the energy, linear momentum, angular momentum and boost momentum of a molecule to order $1/c^2$, where it necessary to take account of kinetic contributions made by the electrons and nuclei as…
Different (not only by sign) affine connections are introduced for contravariant and covariant tensor fields over a differentiable manifold by means of a non-canonical contraction operator, defining the notion dual bases and commuting with…
A rigorous quantum description of molecular dynamics with a particular emphasis on internal observables is developed accounting explicitly for kinetic couplings between nuclei and electrons. Rotational modes are treated in a genuinely…
We present a new type of energy-momentum tensor and angular momentum tensor. They are motivated by a special consideration in quantum measurement: Given a wave in mutual eigen-state of more than one physical observables, the corresponding…
The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…
We propose a single phase-only optical element that transforms different orbital angular momentum (OAM) modes into localized spots at separated angular positions on a transverse plane. We refer to this element as an angular lens since it…
An important methodological problem of theoretical mechanics related to inertia is discussed. Analysis Inertia is performed in four-dimensional Minkowski space-time based on the law of conservation of energy-momentum. This approach allows…
This paper presents some ideas which might assist teachers incorporating special relativity into an introductory physics curriculum. One can define the proper-time/velocity pair, as well as the coordinate-time/velocity pair, of a traveler…
It is shown that, contrary to what is normally expected, it is possible to have angular momentum effects on the geometry of space time at the laboratory scale, much bigger than the purely Newtonian effects. This is due to the fact that the…
Angular momenta of electromagnetic waves are important both in concepts and applications. In this work, we systematically discuss two types of angular momenta, i.e., spin angular momentum and orbital angular momentum in various cases, e.g.,…
The role of the parameter `$a$' associated with the Kerr metric which represents the angular momentum per unit mass of a rotating massive object has been converted into determining the rotationally induced quadrapole electric field outside…
Since gravitational waves are solutions of Einstein's field equations with a zero stress-energy tensor, the reality of these waves was questioned. To demonstrate it, the momentum imparted to test particles by such waves was evaluated. A…
We advance an universal approach to the construction of kinematics in non-inertial and, in particular, rotating reference frames. On its basis a 10-dimensional space including three projections of velocity vector and three turn angles in…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
We suggest a somewhat non-standard view on a set of curious, paradoxical from the standpoint of simple classical physics and everyday experience phenomena. There are the quantisation (discrete set of values) of the observables (e.g.,…