Topological effects of cosmic string on radial eigenvalue solution with Mie-type potential

In this contribution, we study the non-relativistic Schrödinger equation with the interaction potential of Mie-type in the background of the topological defects produced by a cosmic string. We determine the radial eigenvalue solution and analyze the effects of the topological defect. It is shown there that the energy levels and wave function of the non-relativistic quantum particles get modified by the topological defect of the geometry compared to the flat space result with this potential. Afterwards, this eigenvalue solution is utilized in some well-known molecular potential models (Kratzer, modified Kratzer, Coulomb potentials), and presents the eigenvalue solutions.

The time-independent Schrodinger wave equation with potential \((V(r)=\frac{\delta }{r}+\frac{\gamma }{r}^{2} +V_{0})\) in curved space is described by the wave equation \(\left[ -\frac{1}{2\,M}\frac{1}{\sqrt{g}}\partial _{i}(\sqrt{g}g^{ij}\partial _{j})+\left( \frac{\delta }{r}+\frac{\gamma }{r}^{2} +V_{0}\right) \right] \Psi =E \Psi \).