Bound States of the Klein-Gordon for Exponential-Type Potentials in D-Dimensions

Abstract

The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any arbitrary orbital quantum number l and dimensional space D. The relativistic/non-relativistic energy spectrum formula and the corresponding un-normalized radial wave functions, expressed in terms of the Jacobi polynomials

Relativistic Bound States of Spinless Particle by the Cornell Potential Model in External Fields

“…The relativistic bound state solutions can also be obtained in this work for any mixture with ( ) = ( ), where | | ≤ 1. The significance of this bound on | | is the existence of energy eigenvalues (see [60][61][62][63][64] and references therein). The choice of the case = 1 is simply to reduce our solution to the nonrelativistic (Schrodinger) energy states of the single particle.…”

Klein–Gordon Solutions for a Yukawa-like Potential

“…Let us now consider the (3 + 1)-dimensional timeindependent KG equation describing a scalar particle with Lorentz scalar S(r) and Lorentz vector V (r) potentials which takes the form [53,54] …”

“…In addition, we take the interaction potential as in (1) and decompose the total wave function ψ KG (r), with a given angular momentum l, as a product of a radial wave function R l (r) = g(r)/r, and the angular dependent spherical harmonic functions Y m l ( r ) [54] …”

Spinless Particles Subject to Unequal Scalar-Vector Nuclear Woods– Saxon Potentials in Arbitrary Dimensions

“…Also, β is an arbitrary constant demonstrating the ratio of scalar potential to vector potential [17]. When β = 1, it represents the case of spinless particle in equal mixture potentials, i.e., S(r) = V (r), which is being equivalent to the spin-1/2 fermion in the exact spin symmetric limit ∆ (r) = S(r) − V (r) = 0 (the potential difference is exactly zero).…”