Modified Klein–Gordon oscillator in Ellis-Bronnikov-type wormhole spacetime with cosmic string and global monopole

Abstract In this paper, we investigate the modified relativistic oscillator with the Cornell potential via the quadri-potential given by X μ = (0, mωr + A / r , 0, 0) in the Ellis-Bronnikov-type wormhole spacetime with a global monopole and a cosmic string. We obtain the angular and radial wave functions exactly, as well as the eigenenergies. The radial wave function is expressed in terms of Heun polynomials, involving the quantum number n and the eigenenergies. By setting the value of n incrementally, the oscillation frequency ω is quantized with respect to l and m . Finally, as an example, we analyze the ground state and graphically investigate the influence of the global monopole, cosmic string, and A on the oscillator frequency, eigenenergies, and radial probability density, as well as the effect of the wormhole curvature on the radial probability density.