In the present paper, we describe a method of introducing the harmonic oscillator potential into the Klein-Gordon equation, leading to genuine bound states. The eigenfunctions and eigenenergies are worked out explicitly.

No abstract

One-dimensional Klein–Gordon equation with screened Coulomb potential generates genuine bound states in the scalar coupling scheme. In this article we have obtained the exact solutions of the problem. The results are compared with those of the vector coupling scheme.

While the usual harmonic oscillator potential gives discrete energies in the nonrelativistic case, it does not however give genuine bound states in the relativistic case if the potential is treated in the usual way. In the present article, we have obtained the eigenfunctions of the Dirac oscillator in two spatial dimensions, adapting the prescription of Moshinsky.

In this paper we illustrate the existence of genuine bound states for a Dirac particle interacting with a scalar screened Coulomb potential in a 1 + 1 dimension. In contrast to the bare Coulomb potential, the screened Coulomb potential can bind both spin-zero and spin-1/2 particles in the scalar prescription.