Related papers: Remarks on the Theory of Angular Momenta
The uncertainty relation between angle and orbital angular momentum had not been formulated in a similar form as the uncertainty relation between position and linear momentum because the angle variable is not represented by a quantum…
In quantum mechanics textbooks the momentum operator is defined in the Cartesian coordinates and rarely the form of the momentum operator in spherical polar coordinates is discussed. Consequently one always generalizes the Cartesian…
We discuss the requirement of single valuedness and periodicity of eigenfunction of the third component of the operator of angular momentum. This condition, imposed on a non observable, is often used to derive that the eigenvalues of…
Eigenfunctions and eigenvalues of the operator of the square of the angular momentum are studied. It is shown that neither from the requirement for the eigenfunctions be normalizable nor from the commutation relations it is possible to…
It is shown that when the gauge-invariant Bohr-Rosenfeld commutators of the free electromagnetic field are applied to the expressions for the linear and angular momentum of the electromagnetic field interpreted as operators then, in the…
Based on the novel prescription for the power of a complex number, a new expression for the eigenfunction of the operator of the third component of the angular momentum is presented. These functions are normalizable, single valued and are…
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…
Invoking Maxwell's classical equations in conjunction with expressions for the electromagnetic (EM) energy, momentum, force, and torque, we use a few simple examples to demonstrate the nature of the EM angular momentum. The energy and the…
The flux of angular momentum of electromagnetic field of an arbitrarily moving point charge is investigated. General equations are obtained for the transfer of angular momentum at arbitrary distance from the charge, and corresponding…
The eigenfunctions and eigenvalues of orbital angular momentum operator on noncommutative lattice for a circle poset by theta-quantization are constructed, and it is demonstrated that they are equivalent to those of the conventional quantum…
Suppose a classical electron is confined to move in the $xy$ plane under the influence of a constant magnetic field in the positive $z$ direction. It then traverses a circular orbit with a fixed positive angular momentum $L_z$ with respect…
Complex and spinorial techniques of general relativity are used to determine all the states of the $SU(2)$ invariant quantum mechanical systems in which the equality holds in the uncertainty relations for the components of the angular…
A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form…
The motion of a system of particles under electromagnetic interaction is considered. Under the assumption that the force acting on an electric charge is given by the sum of the electromagnetic fields produced by any other charged particles…
As is widely-known, the eigen-functions of the Landau problem in the symmetric gauge are specified by two quantum numbers. The first is the familiar Landau quantum number $n$, whereas the second is the magnetic quantum number $m$, which is…
The Hilbert space of states of the relativistic Majorana particle consists of normalizable bispinors with real components, and the usual momentum operator $- i \nabla$ can not be defined in this space. For this reason, we introduce the…
The angular momentum of radiation from an arbitrarily moving relativistic charge is studied. The angular momentum is presented as the sum of the angular momentum relative to the point where the charge is located at a retarded moment of time…
By means of the Helmholtz theorem on the decomposition of vector fields, the angular momentum of the classical electromagnetic field is decomposed, in a general and manifestly gauge invariant manner, into a spin component and an orbital…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…