Morris–Thorne-type wormhole with a cosmic string effects on harmonic oscillator problem

In this study, we explore quantum dynamics of non-relativistic particles within the context of a Morris–Thorne-type wormhole space-time featuring a cosmic string. Our investigation focuses on the eigenvalue solution of Schrödinger equation by utilizing the confluent Heun equation. We demonstrate that the cosmic string and the wormhole throat radius leads to significant modifications in the energy levels and wave functions of non-relativistic quantum particles. As a consequence, the degeneracy of the energy spectrum is disrupted. Subsequently, we extend our analysis to the harmonic oscillator problem, where non-relativistic particles interact harmonically within the same wormhole space-time background with a cosmic string. Employing a similar approach, we obtain the eigenvalue solution for the harmonic oscillator and analyze this solution to show the influence of the cosmic string parameter and the radius of the wormhole throat. In both scenarios, we obtain exact analytical solutions for the wave equation and specifically, we present the ground-state energy level \(E_{1,m}\) $E_{1,m}$ and the corresponding wave function \(\psi _{1,m}\) ${\psi }_{1,m}$ as particular cases.