Solutions of the three-dimensional radial Dirac equation from the Schrödinger equation with one-dimensional Morse potential

Abstract

New exact analytical bound-state solutions of the radial Dirac equation in 3+1 dimensions for two sets of couplings and radial potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the onedimensional generalized Morse potential. The eigenfunctions are expressed in terms of generalized Laguerre polynomials, and the eigenenergies are expressed in terms of solutions of equations that can be transformed into polynomial equations. Several analytical results found in the literature, including the Dirac oscillator, are obtained as particular cases of this unified approach.

Pure Coulomb tensor interaction in the Dirac equation

“…The time-independent Dirac equation for a spin 1/2 particle with mass M interacting with a tensor potential U is given by [6]…”

“…we may write the radial equation for upper and lower radial functions of the Dirac spinor g κ (r) and f κ (r) as [6]:…”

“…A recent paper by some of the authors deals also with a similar problem in the more general context of a mapping from an one-dimensional Schroedinger equation with a Morse potential [6].…”

“…We will follow closely the formalism of ref. [6] in computing the solutions. The paper is organized as follows: following the present introduction, in sec.…”

Morse potential in relativistic contexts from generalized momentum operator, Pekeris approximation revisited and mapping

“…The goal of this letter is to extend the strategy used in [20] to the 1D and 3D KG and Dirac oscillators in order to obtain the corresponding relativistic equations for a Morse potential coupling [23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]. The letter is structured as follows.…”