Coupled modes semiclassical treatment of nonadiabatic transitions

Abstract

We analyse the Schrodinger wave equation of a two-level or spinorial Hamiltonian, from a classical point of view. An iterative scheme, the coupled mode semiclassical formalism, is proposed, allowing us to deal with the nonadiabatic transfer. As the WKB expansion, it allows the one-dimensional Schrodinger equation to be integrated by successive quadratures. Finally, we show that time-dependent information can be drawn from the previous, purely stationary, analysis by extending the notion of group velocity. The proposed formalism is thus coherent with an image of multiple trajectories, conforming more to physical behaviour than a single trajectory.