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.

在本文中，我们研究了在包含位错的宇宙弦时空中存在排斥平方反比势的情况下量子谐振子的行为。我们的目标是通过汇合超几何函数解析求解薛定谔波动方程，找到该量子系统的特征值解。此外，我们还探讨了旋转框架对这种特定时空几何结构内的量子谐振子的影响，并结合了相同的排斥势。按照类似的过程，我们成功地确定了该量子系统的特征值解。重要的是，我们的结果表明，特征值解受到四个关键参数的显着影响：宇宙弦、与几何相关的位错参数、排斥平方反比势和旋转框架的恒定角速度。这些参数的存在会引起能谱的变化，从而导致量子谐振子的行为与已知结果相比发生变化。