Related papers: Spinors and Rodrigues representations associated w…
We consider the representations of the optical Dirac equation, especially ones where the Hamiltonian is purely real-valued. This is equivalent, for Maxwell's equations, to the Majorana representation of the massless Dirac (Weyl) equation.…
We consider Schr\"{o}dinger equations with linearly energy-depending potentials which are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under…
On the basis of the Wigner unitary representations of the covering group ISL(2,C) of the Poincar\'{e} group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the…
All relativistic corrections to the Scr{\"o}dinger equation which determine the interlink between spin and orbit of moving particles, are directly calculated from the Dirac equation using the spin invariant operators. It is shown that among…
The Dirac monopole string is specified for de Sitter cosmological model. Dirac equation for spin 1/2 particle in presence of this monopole has been examined on the background of de Sitter space-time in static coordinates. Instead of spinor…
It has been suggested that the high symmetries in the Schr\"odinger equation with the Coulomb or harmonic oscillator potentials may remain in the corresponding relativistic Dirac equation. If the principle is correct, in the Dirac equation…
The Nikiforov-Uvarov polynomial method employed by Aguda to solve the Dirac equation with an improved Rosen-Morse potential plus a Coulomb-like tensor potential is shown inappropriate because the conditions of its application are not…
A new discretization of the radial equations that appear in the solution of separable second order partial differential equations with some rotational symmetry (as the Schrodinger equation in a central potential) is presented. It cures a…
We generalize our previous unification of the Schrodinger and guidance equations in a single inhomogeneous Schrodinger equation to a Riemannian manifold with an external vector potential. A special case yields the unified theory for a spin…
We obtain the energy eigenvalues and radial wave functions of the D-Dimensional Dirac equation in the case of spin symmetry for Woods-Saxon potential in minimal length formalism. The radial part of the D-Dimensional Dirac equation is solved…
A consistent variational derivation of the Majorana 4-spinor field equations coupled to Einstein's theory of gravitation is given. The equivalence of the first and the second order variational field equations is explicitly demonstrated. The…
The analytical relations in position, momentum and four-dimensional spaces are established for the expansion and one-range addition theorems of relativistic complete orthonormal sets of exponential type spinor wave functions and Slater…
The approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen-Morse potentials including the spin-orbit centrifugal (pseudo-centrifugal) term are obtained. Under the conditions of spin and pseudospin…
The bispinor wave function finds its fundamental application in the study of electrons, neutrinos and protons as particles bound by their own potentials. Classical electromagnetism and the Dirac electron theory appear to be natural…
A relation between classical electrostatic fields and Schr\"odinger-like Hamiltonians is evidenced. Hence, supersymmetric quantum potentials analogous to classical electrostatic fields can be constructed. Proposing an ansatz for the…
In this paper we present a unified approach to the spectral analysis of an hypergeometric type operator whose eigenfunctions include the classical orthogonal polynomials. We write the eigenfunctions of this operator by means of a new Taylor…
The presentation makes use of geometric algebra, also known as Clifford algebra, in 5-dimensional spacetime. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from…
The spinorial degrees of freedom of two or more spacelike separated Dirac particles are considered and a method for constructing mixed polynomials that are invariant under the spinor representations of the local proper orthochronous Lorentz…
In the framework of the Joos-Weinberg 2(2S+1)- theory for massless particles, the dynamical invariants have been derived from the Lagrangian density which is considered to be a 4- vector. A la Majorana interpretation of the 6- component…
It is shown that the Dirac equation with the Coulomb potential can be solved using the algebra of the three spinor invariants of the Dirac equation without the involvement of the methods of supersymmetric quantum mechanics. The Dirac…