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In this paper, we investigate the relativistic harmonic oscillator in the Ellis–Bronnikov-type wormhole spacetime with a global monopole and cosmic string. We obtain the angular and radial wave functions exactly as well as the eigenenergies. Additionally, the radial wave function is expressed in terms of Heun polynomial, and as a consequence, the oscillation frequency is quantized. Finally, we graphically analyze the influence of the wormhole, as well as the influence of the global monopole and cosmic string on the radial probability density and the eigenenergies.
Oliveira et al. (Wed,) studied this question.