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

Abstract

Exact analytical solution to the relativistic Klein-Gordon equation with noncentral equal scalar and vector potentialsAbstract. The solutions of the Klein-Gordon equation with equal scalar and vector harmonic oscillator plus inverse quadratic potential for S-waves have been presented using the Nikiforov-Uvarov method. The bound state energy eigenvalues and the corresponding un-normalized eigenfunctions are obtained in terms of the Laguerre polynomials.

From the nonrelativistic Morse potential to a unified treatment of a large class of bound‐state solutions of a modified D‐dimensional Klein–Gordon equation

“…This class represents a generalization of the cases found in Wen‐Chao () ( V r = V 0 = 0 and V v = V s = γ s r 2 in three dimensions), Wen‐Chao () and Zhang & Chen () ( V r = V 0 = 0 and V v = V s = γ s r 2 in two dimensions), Ita et al () ( V r = V 0 = 0 and V v = V s = α s / r 2 + γ s r 2 for S ‐waves in three dimensions), Ikhdair & Hamzavi () ( V r = V 0 = 0 and the pseudo‐harmonic potential in two dimensions) and Bruce & Minning () ( V 0 = V v = V s = 0 and β r = 0, as a matter of fact the space component of a nonminimal vector anisotropic linear potential in three dimensions).…”

New solutions of the D-dimensional Klein–Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential

“…This class represents a generalization of the cases found in [41] (V r = V 0 = 0 and V v = V s = γ s r 2 in three dimensions), [42] and [43] (V r = V 0 = 0 and V v = V s = γ s r 2 in two dimensions), [44] (V r = V 0 = 0 and V v = V s = α s /r 2 + γ s r 2 for S -waves in three dimensions), [45] (V r = V 0 = 0 and the pseudo-harmonic potential in two dimensions) and [55] (V 0 = V v = V s = 0 and β r = 0, as a matter of fact the space component of a nonminimal vector anisotropic linear potential in three dimensions). The complete identification with the generalized Morse potential is done with the identifications…”

“…From now on the time component of the vector potential will be denominated by V v in this paper. The equal-magnitude mixing of vector and scalar couplings for arbitrary angular momentum has been considered for the harmonic oscillator [41][42][43], for S -waves of the SHO [44] and for arbitrary angular momentum for the pseudo-harmonic potential (a special particular case of the SHO) [45]. The Coulomb potential has been studied as a vector coupling [46][47][48], scalar coupling [47,48], mixing of vector and scalar couplings with equal magnitudes [43], and an arbitrary mixing of vector and scalar couplings [49][50][51].…”

Solution of Q-Deformed D-Dimensional Klein-Gordon Equation Kratzer Potential using Hypergeometric Method

“…In quantum mechanics, the effect of relativistic should be considered when a particle moving in strong potential [1,2]. Klein-Gordon and Dirac equations describe the dynamic of particles in relativistic quantum mechanics.…”