Related papers: Comment on Solution of the Relativistic Dirac-Mors…
PT-/non-PT-symmetric and non-Hermitian deformed Morse and Poschl-Teller potentials are studied first time by quantum Hamilton-Jacobi approach. Energy eigenvalues and eigenfunctions are obtained by solving quantum Hamilton-Jacobi equation.
Exact solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic…
In this comment it is argued that the argument for a unique determination of the electromagnetic potentials in classical electrodynamics in [1] is flawed. To the contrary the "gauge freedom" of the electromagnetic potentials has proven as…
The exact solutions of the one-dimensional Klein-Gordon equation for the Rosen-Morse type potential with equal scalar and vector potentials are presented. First we briefly review Nikiforov-Uvarov mathematical method. Using this method,…
This work is concerned about introducing two new 1D and 3D confined potentials and present their solutions using the Tridiagonal Representation Approach (TRA). The wavefunction is written as a series in terms of square integrable basis…
This work aims to shed some light on the meaning of the positive energy assumption in relativistic quantum theory and its relation to questions of localization of quantum systems. It is shown that the positive energy property of solutions…
The current paper discusses and analytically solves the Langmuir spherical problem. A general solution has been obtained in a parametric representation and expressed in terms of the Airy function. A solution to the electric potential in a…
The relativistic 2-body problem, much like the non-relativistic one, is reduced to describing the motion of an effective particle in an external field. The concept of a relativistic reduced mass and effective particle energy introduced some…
The relativistic positive-energy wave equation proposed by P. Dirac in 1971 is an old but largely forgotten subject. The purpose of this note is to speculate that particles described by this equation (called here Dirac particles) are…
Morse theoretical ideas are applied to the study of relative equilibria in the planar $n$-vortex problem. For the case of positive circulations, we prove that the Morse index of a critical point of the Hamiltonian restricted to a level…
We extend the classical Pohozaev's identity to semilinear elliptic systems of Hamiltonian type, providing a simpler approach, and a generalization, of the results of E. Mitidieri [6], R.C.A.M. Van der Vorst [14], and Y. Bozhkov and E.…
In 1892 H.A. Lorentz started the search for a classical equation of motion for pointlike charged particles that takes into account the radiation reaction force. This search culminated in the Lorentz-Abraham-Dirac equation of motion, which…
The concept of the elegant work introduced by Levai in Ref. [5] is extended for the solutions of the Schrodinger equation with more realistic other potentials used in different disciplines of physics. The connection between the present…
A Hamiltonian formulation for the classical problem of electromagnetic interaction of two charged relativistic particles is found.
The modern theory of the potential does not give a solution of Poisson's equation. In the present work its solution has been found via generalized functions and a nonpotential solution of the continuity equation has been obtained. The…
In this paper we present for the first time a complete description of the Bohm model of the Dirac particle. This result demonstrates again that the common perception that it is not possible to construct a fully relativistic version of the…
An exact solution is given to the classical electromagnetic (EM) radiation-reaction (RR) problem, originally posed by Lorentz. This refers to the dynamics of classical non-rotating and quasi-rigid finite size particles subject to an…
The non-relativistic Goedecke equation (1975), which describes the motion of a point charge taking into account the radiation reaction, has no "runaway" solutions. A "physical" method of covariant generalization of this equation is…
Some exact analytical formulas are derived for the potential and mass ratio as a function of Lagrangian points position, in the classical Roche model of the close binary stars.
Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by…