On a Particle Confined to the Squared Cotangent Potential in the Global Monopole Spacetime

We study the confinement of a quantum particle to the squared cotangent potential in the background of global monopole spacetime. By dealing with s-states, we obtain the energy levels from the exact solutions to the Schrödinger equation. Then, we show that the topology of the global monopole spacetime influences the energy levels. Further, we show that there is a non-null revival time with regard to the squared cotangent potential and how it is influenced by the global monopole topology.