Bound states of relativistic particles in reflectionless-type potential

Abstract

The s-wave bound states of Klein-Gordon equation and Dirac equation with scalar and vector reflectionless-type potentials are obtained.

Analytical Study of the Behavioral Trend of Klein-Gordon Equation in Different Potentials

“…With this, it still requires the use of good mathematical methods such as the variational method, functional analysis, supers metric approach, Nikiforov-Uvarov (NU, the asymptotic iteration method and so on In recent period, work has been carried out on to study bound state of KGE for a number of special potentials [1,15] even in the case of equal vector and scalar potential [16], because it reduces KGE to a Schrodinger type of equation which could in turn be transformed into hypergeometric differential equation that has a known solution using [17][18][19][20] and this is more reason why KGE is receiving attention considerably in the literature when it comes to use of potentials [21,22]. In fact it has been shown that exact solution are possible with some certain central potentials [23][24][25][26] which has help in investigation of bound states of the KGE for that particular potential which on the other hand has invariably led to derivation of the exact expression of the energy eigenvalues and the corresponding normalized eigenfunctionns in terms of some special polynomials and hypergeometrical function [16,[27][28][29].…”

SUSYQM and SWKB Approaches to the Relativistic Equations with Hyperbolic PotentialV0tanh2(r/d)

“…With the recent interest in the relativistic equations with some physical potentials, many authors have solved the Klein-Gordon and Dirac equations with some typical potentials provided that the scalar potential is equal to the vector potential, such as the Hulthén potential [18,19,20], the Morse potential [21], the Wood-Saxon potential [22], the tan 2 ( r) potential [23], the Pöschl-Teller, the reflection-less type potential [24,25] and the harmonic oscillator potential and others [26]. It should be noted that Chen [27] has solved the Klein-Gordon and Dirac equations with the pseudoharmonic oscillator potential using SUSY and shape invariance approaches.…”