Non-adiabatic corrections to the method of stationary states

Yu. S. Tyupkin, A. S. Shvart︠s︡

G. F. Drukarev

Takahiro Yamaguchi

Stimulated Raman adiabatic passage method (STIRAP) is well known to be a very effective method for the efficient and selective transition between two molecular eigenstates in molecule. In this study, we generalize the STIRAP to be able to treat the transition to the non‐stationary state in the hydrogen bonded model system.

Andrei Gaidash, E. E. Memekh, George P. Miroshnichenko +1 more

This work examines a non-stationary phase-modulation process characterized by a time-dependent interaction coefficient, confined to the non-degenerate case. We derive an exact non-adiabatic solution to the time-dependent Schro¨ dinger equation. We then establish the criterion under which adiabatic considerations become valid-specifically, the condition permitting a stationary-state solution to approximate the non-stationary problem. Our results hold for an arbitrary number of interacting modes and an arbitrary photon number.

Vladimir I. Osherov

Vladimir Mitin, Dmitry I. Sementsov, Nizami Z. Vagidov

The solution of most problems associated with electron quantum states in physical systems and structures (atoms, molecules, quantum nanostructure objects, and crystals) is hard to find because of the mathematical difficulties of getting exact solutions of the Schrödinger equation. Therefore, approximate methods of solving such problems are of special interest. We will consider some of these methods, such as the adiabatic approximation now and later the effective-mass method , using real physical systems as examples. In this chapter we will consider several widely used approximation methods for finding the wavefunctions and energies of quantum states as well as the probabilities of transitions between quantum states. First of all, we will consider stationary and non-stationary perturbation theories. What is common to these two theories is that it is assumed that the perturbation is weak and that it changes negligibly the state of the unperturbed system. Stationary perturbation theory is used for the approximate description of a system's behavior if the Hamiltonian of the quantum system being considered does not directly depend on time. In the opposite case, non-stationary theory is used. Then, we will briefly consider the quasiclassical approximation, which is used for the problems of quantum mechanics which are close to analogous problems of classical mechanics. Stationary perturbation theory for a system with non-degenerate states This theory is used for the approximate calculation of the energy levels and the wavefunctions of stationary states of systems that are subjected to the influence of small perturbations.