Abstract
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.
Highlights
Idealized physical systems are of interest in the most textbooks of classical and quantum mechanics, a large part of actual physical systems are more complicated and described by time-dependent Hamiltonians
The invariant operator method is very useful when we investigate quantum mechanical features of time-dependent Hamiltonian system (TDHS), because of the fact that the Schrodinger solutions of a TDHS can be represented in terms of the eigenstates of the invariant operator.[21]
The potential we have considered is composed of the inverse quadratic potential and the Coulomb potential
Summary
Idealized physical systems are of interest in the most textbooks of classical and quantum mechanics, a large part of actual physical systems are more complicated and described by time-dependent Hamiltonians. We investigate quantum features of a three-dimensional time-dependent non-central potential system in this work, where there are singularities in the governing potentials of the system. The consideration of non-central features of potentials associated with molecular dynamics is necessary for obtaining better results in the classical and quantum analyses for the molecular structures and interactions between the molecules.[13,14] The potential we consider in this work is a combination of two singular potentials which are the inverse quadratic potential and the Coulomb potential. Starting from a general quantum description of the time-dependent non-central potential system, quantum features of the system based on Schrodinger solutions will be investigated. The invariant operator method is very useful when we investigate quantum mechanical features of TDHSs, because of the fact that the Schrodinger solutions of a TDHS can be represented in terms of the eigenstates of the invariant operator.[21]
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