Quantum features of molecular interactions associated with time-dependent non-central potentials

Abstract

The research for quantum features of molecular Coulomb interactions subjected to a time-dependent non-central potential has many applications. The wave functions of this system can be obtained by using an invariant operator, which is necessary for investigating a time-dependent Hamiltonian system. Regarding time dependence of the system, one can confirm that the formula of this operator is in general somewhat complicated. Hence, in order to solve its eigenvalue equation, special mathematical techniques beyond separation of variables method, such as the unitary transformation method, the Nikiforov-Uvarov method, and the asymptotic iteration method, should be employed. The double ring-shaped generalized non-central potential of which evolution explicitly depends on time is introduced as a particular case. The complete quantum solutions of the system can be identified from the eigenstates of the invariant operator. These solutions are useful for analyzing dynamical properties of the system.

Dynamics of free time-dependent effective mass

“…For a TDEM, the system becomes non-conservative [34,35]. In particular, if a quantum system interacts with time-varying environments such as temperature, pressure, stress, and energy, the effective masses will be modified by some TDEM [34][35][36][37][38][39]. A first principle calculation for the viable Hamiltonian of a position and time-dependent effective mass was proposed in [31].…”