Harmonic Oscillator in Cosmic String Space-Time with Dislocation Under a Repulsive $$1/r^2$$ Potential and Rotational Frame Effects

In this paper, we investigate the behavior of a quantum harmonic oscillator in the presence of a repulsive inverse-square potential within a cosmic string space-time that contains a dislocation. Our objective is to find eigenvalue solutions of this quantum system by analytically solving the Schrödinger wave equation through the confluent hypergeometric function. Furthermore, we explore the effects of a rotational frame on the quantum harmonic oscillator within this specific space-time geometry, incorporating the same repulsive potential. Following a similar procedure, we successfully determine the eigenvalue solutions for this quantum system. Importantly, our results reveal that the eigenvalue solutions are significantly influenced by four key parameters: the cosmic string, the dislocation parameter associated with the geometry, the repulsive inverse-square potential, and the constant angular speed of the rotating frame. The presence of these parameters induces a shift in the energy spectrum, thereby causing modifications to the behavior of the quantum harmonic oscillator compared to the known results.