Quantization of time-dependent singular potential systems: Non-central potential in three dimensions

Quantum features of a dynamical system subjected to time-dependent non-central potentials are investigated. The entire potential of the system is composed of the inverse quadratic potential and the Coulomb potential. An invariant operator that enables us to treat the time-dependent Hamiltonian system in view of quantum mechanics is introduced in order to derive Schrödinger solutions (wave functions) of the system. To simplify the problem, the invariant operator is transformed to a simple form by unitary transformation. Quantum solutions in the transformed system are easily obtained because the transformed invariant operator is a time-independent simple one. The Nikiforov-Uvarov method is used for solving eigenvalue equation of the transformed invariant operator. The double ring-shaped generalized non-central time-dependent potential is considered as a particular case for further study. From inverse transformation of quantum solutions obtained in the transformed system, the complete quantum solutions in the original system are identified. The quantum properties of the system are addressed on the basis of the wave functions.