Bound state solutions of the Klein - Gordon equation for deformed Hulthen potential with position dependent mass

Abstract

We solve approximately the bound state solutions of the Klein -Gordon equation for deformed Hulthen potential with unequal scalar and vector potential for arbitrary  l state. We obtain explicitly the energy eigenvalues and the corresponding wave function expressed in terms of the Jacobi polynomials. We also discuss the energy eigenvalues of our result for three cases with equal and unequal scalar and vector potentials.

Solutions of the Klein-Gordon equation with equal scalar and vector harmonic oscillator plus inverse quadratic potential

“…with being at most first order polynomials. Also, the hypergeometric-type functions in equation (5) for a fixed integer is given by the Rodrigue relation as (7) where is the normalization constant and the weight function must satisfy the condition (8) with (9) In order to accomplish the condition imposed on the weight function it is necessary that the polynomial be equal to zero at some point of an interval and its derivative at this interval at will be negative [30].…”

“…For . We obtain from equation (9) and the derivative of this expression would be negative, i.e., . From equations (12) and (13) we obtain ,…”

“…These solutions could be exact or approximate and they normally contain all the necessary information for the quantum system. Quite recently, several authors have tried to solve the problem of obtaining exact or approximate solutions of the KG equation for a number of special potentials using different methods [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Some of these potentials are known to play very important roles in many fields of Physics such as Molecular Physics, Solid State and Chemical Physics [21].…”

Relativistic Study of Spinless Particles for Generalized Hylleraas Potential with Position Dependent Mass

“…In nuclear and high energy physics, one of the interesting problems is to obtain exact solution of the Klein-Gordon, Duffin-Kemmer-Petiau and Dirac equations. When a particle is in a strong potential field, the relativistic effect must be considered, which gives the correction for nonrelativistic quantum mechanics [14,15].…”

Relativistic Treatment of Massive Klein-Gordon Particle by Modified Generalized Hulthen Potential

“…Recently, many studies have been carried out to explore the relativistic energy eigenvalues and corresponding wave functions of the Klein-Gordon and Dirac equations [14,20,21]. The aim of this paper is to obtain the energy eigenvlaues and the corresponding eigen functions for the massive Klein-Gordon particle under modified generalized Hulthen potential in a case of equal scalar and vector using the parametric generalization of the Nikiforov-Uvarov (NU) method.…”