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We discuss a previously unpublished description of electromagnetism outlined by Richard P. Feynman in the 1960s in five handwritten pages, recently uncovered among his papers, and partly developed in later lectures. Though similar to the…
On the seminal paper written by Einstein, Podolsky and Rosen [1], a critique to the completeness of quantum mechanics was posed. Part of the critique consisted in the following argument: if quantum mechanics is complete, then, two physical…
We represent in this note the solutions of the electronic Schr\"odinger equation as traces of higher-dimensional functions. This allows to decouple the electron-electron interaction potential but comes at the price of a degenerate elliptic…
The Maxwell vector potential and the Dirac spinor used to describe the classical theory of electrodynamics both have components which are considered to be ordinary smooth functions on space-time. We reformulate electrodynamics by adding an…
General relations for electromagnetic field energy outside the transparency domain are proposed. It is shown that charged particle contribution to the energy of electromagnetic perturbations in the general case can be described in terms of…
This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: they are forbidden by very general…
In this paper, we define a scalar complex potential $\mathcal{S}$ for an arbitrary electromagnetic field. This potential is a modification of the two scalar potential functions introduced by E. T. Whittaker. By use of a complexified…
Recently, several discussions on the possible observability of 4-vector potential have been published in literature. Furthermore, several authors recently claimed existence of the helicity=0 electromagnetic field. We re-examine the theory…
The concept of complex harmonic potential in a doubly connected condenser (capacitor) is introduced as an analogue of the real-valued potential of an electrostatic vector field. In this analogy the full differential of a complex potential…
This article contains a digest of the theory of electromagnetism and a review of the transformation between inertial frames, especially under low speed limits. The covariant nature of the Maxwell's equations is explained using the…
This article is devoted to the spectral analysis of the electro-magnetic Schr\"odinger operator on the Euclidean plane. In the semiclassical limit, we derive a pseudo-differential effective operator that allows us to describe the spectrum…
The Laplace's equations for the scalar and vector potentials describing electric or magnetic fields in cylindrical coordinates with translational invariance along azimuthal coordinate are considered. The series of special functions which,…
We show that the formalism of supersymmetric quantum mechanics applied to the solvable elliptic function potentials $V(x) = mj(j+1){sn}^2(x,m)$ produces new exactly solvable one-dimensional periodic potentials.
All the concepts and principles necessary to understand quantum mechanics on an initial level are given in a form suitable for the non-expert. The concepts explained include visualizing the wave function, wave-particle duality, the…
We present a new explanation for a quantum eraser. Mathematical description of the traditional explanation needs quantum-superposition states. However, the phenomenon can be explained without quantum-superposition states by introducing…
An exponential polynomial is a finite linear sum of terms $P(z)e^{Q(z)}$, where $P(z)$ and $Q(z)$ are polynomials. The early results on the value distribution of exponential polynomials can be traced back to Georg P\'olya's paper published…
We outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly…
In the broken-symmetry phase of the electroweak theory there is no unique definition of the electromagnetic field tensor in cases where the magnitude of the Higgs field differs from a constant value. The meaning of the electromagnetic field…
In this article it is reported a formulation of the solenoidal nature of quantum electronic currents at the nanoscale whose divergence is expressed as the coupling of a magnetic field, interacting with a quantum body, and a weighted Cern…
This paper deals with the old yet unsolved problem of defining and evaluating the stored electromagnetic energy - a quantity essential for calculating the quality factor, which reflects the intrinsic bandwidth of the considered…