Related papers: Dirac oscillators and the relativistic R matrix
We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary…
We proceed with the construction of normalizable Dirac wave packets for treating chiral oscillations in the presence of an external magnetic field. Both chirality and helicity quantum numbers correspond to variables of fundamental…
A reduced form of the Dirac equation has been previously introduced and studied in the Center of Mass reference frame. In this work we show that this equation can be written in a covariant form in a generic reference frame by using specific…
The Dirac equation provides a description of spin 1/2 particles, consistent with both the principles of quantum mechanics and of special relativity. Often its presentation to students is based on mathematical propositions that may hide the…
We study the dynamics of the 2+1 Dirac oscillator exactly and find spin oscillations due to a {\it Zitterbewegung} of purely relativistic origin. We find an exact mapping of this quantum-relativistic system onto a Jaynes-Cummings model,…
This work comes as the second part in a series of investigations into the dynamics of rotating waves as solutions to lattice dynamical systems. Such nonlinear waves as solutions to mathematical equations are of great interest throughout 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…
As a continuation of previous investigations, the formalism used there is extended to the case when an external electric field is present and the covariant formulation is performed again. The equation system obtained allows no restriction…
We consider the Dirac equation with a generalized uncertainty principle in the presence of the Harmonic interaction and an external magnetic field. By doing the study in the momentum space, the problem solved in an exact analytical manner…
We develop a relativistic model to describe the bound states of positive energy and negative energy in finite nuclei at the same time. Instead of searching for the negative-energy solution of the nucleon's Dirac equation, we solve the Dirac…
This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first…
A relativistic formulation of reaction theory for nuclei with a dynamics given by a unitary representations of the Poincar\'e group is developed. Relativistic dynamics is introduced by starting from a relativistic theory of free particles…
We show that spin-flip probabilities emerge in the relativistic regime for scalar potentials, absent in the standard Dirac representation. We examine 1D scattering for the Dirac equation employing an alternate matrix representation…
The Dirac equation is used to describe oblique spin-conserving and spin-flip reflections of relativistic electrons from a one-dimensional potential barrier in a vacuum. When an electron hits the barrier from an oblique direction, its…
Exact solutions of two-particle relativistic equations of quantum field theory describing the scattering $s$-states and the bound $s$-states are found in the cases of delta-shell potential and superposition of delta-shell potentials. Some…
The magnetic Dirac operator describes the relativistic motion of a charged particle in a magnetic field. Although this operator got a lot of attention in physics many of its fundamental mathematical properties remain unexplored and this…
In this note we discuss the usage of the Dirac $\delta$ function in models of phase oscillators with pulsatile inputs. Many authors use a product of the delta function and the phase response curve in the right hand side of an ODE to…
We construct a tridiagonal matrix representation for the three dimensions Dirac-Coulomb Hamiltonian that provides for a simple and straightforward relativistic extension of the complex scaling method. Besides the Coulomb interaction,…
Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in…
The problem of self-adjoint extensions of Dirac-type operators in manifolds with boundaries is analysed. The boundaries might be regular or non-regular. The latter situation includes point-like interactions, also called delta-like…