Klein–Gordon oscillator with scalar and vector potentials in topologically charged Ellis–Bronnikov-type wormhole
Abbad Moussa, Houcine Aounallah, Prabir Rudra, Faizuddin Ahmed
Abstract
In this work, we study the Klein–Gordon oscillator with equal scalar and vector potentials in a topologically charged Ellis–Bronnikov wormhole space-time background. The behaviour of a relativistic oscillator field is studied with a position-dependent mass via transformation [Formula: see text] and vector potential through a minimal substitution in the wave equation. Simplifying the Klein–Gordon oscillator equation for three different types of potential, such as linear confining, Coulomb-type, and Cornell-type potential and we arrive at a second-order differential equation known as the biconfluent Heun (BCH) equation and the corresponding confluent Heun function. Finally, we solve the wave equation by the Frobenius method as a power series expansion around the origin and obtain the energy levels and the wave function.