Bound states of Klein–Gordon equation for double ring-shaped oscillator scalar and vector potentials

Abstract

In spherical polar coordinates, double ring-shaped oscillator potentials have supersymmetry and shape invariance for θ and r coordinates. Exact bound state solutions of Klein–Gordon equation with equal double ring-shaped oscillator scalar and vector potentials are obtained. The normalized angular wavefunction expressed in terms of Jacobi polynomials and the normalized radial wavefunction expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.