Solutions of the Klein Gordon equation with generalized hyperbolic potential in D-dimensions

Abstract

We solve the D-dimensional Klein-Gordon equation with a newly proposed generalized hyperbolic potential model, under the condition of equal scalar and vector potentials. The relativistic bound state energy equation has been obtained via the functional analysis method. We obtained the relativistic and non-relativistic ro-vibrational energy spectra for different diatomic molecules. The numerical results for these diatomic molecules tend to portray inter-dimensional degeneracy symmetry. Variations of the energy eigenvalues obtained with the potential parameters have been demonstrated graphically. Our studies will find relevant applications in the areas of chemical physics and high-energy physics.

Bound state solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via asymptotic iteration method

“…3 for a given potential model. The corresponding energy eigenvalues are calculated by means of the quantization condition [12][13][14][15][16] .…”

“…The solution of the Schrödinger equation contains all the necessary information needed for the full description of a quantum state such as the probability density and entropy of the system 7,8 . The Schrödinger equation with many physical potentials model have been investigated in recent times with different advance mathematical technique such as Nikiforov-Uvarov (NU) method [9][10][11] , asymptotic iteration method (AIM) [12][13][14][15][16] , functional analysis approach 16 , supersymmetric quantum mechanics (SUSYQM) [17][18][19][20] among others 21 . One of such potential models is the Kratzer potential 22 where D is the dissociation energy and a is the equilibrium internuclear length.…”

Solutions of Schrodinger equation and thermal properties of generalized trigonometric Poschl-Teller potential.

“…Several mathematical approaches have been developed to solve differential equations arising from these considerations. They include the supersymmetric approach [21][22][23][24], Nikiforov-Uvarov method [25][26][27], asymptotic iteration method (AIM) [28][29][30], Feynman integral formalism [31][32][33][34], factorization formalism [35,36], Formula Method [37] exact quantization rule method [38][39][40][41][42][43], proper quantization rule [44][45][46][47][48], Wave Function Ansatz Method [49] etc... The trigonometric Pöschl-Teller potential was proposed by Pöschl and Teller [50] in 1933, and it has been used in describing diatomic molecular vibration.…”

A New Approach to the Approximate Analytic Solution of the Three-Dimensional Schrӧdinger Equation for Hydrogenic and Neutral Atoms in the Generalized Hellmann Potential Model

“…Edet et al obtained analytic solutions of the SE with non-central generalized inverse quadratic Yukawa potential and -deformed Hulthen plus generalized inverse quadratic Yukawa potential in arbitrary dimensions [12,13]. U.S. Okorie et al solved the Klein-Gordon equation (KGE) with a generalized hyperbolic potential in D-dimensions [14]. B.I.…”