Klein–Gordon oscillator with scalar and vector potentials in topologically charged Ellis–Bronnikov-type wormhole

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 relativistic field is studied position-dependent mass via transformation [Formula: see text] potential through minimal substitution wave equation. Simplifying equation for three different types potential, such as linear confining, Coulomb-type, Cornell-type arrive at second-order differential known biconfluent Heun (BCH) corresponding confluent function. Finally, solve by Frobenius method power series expansion around origin obtain energy levels