Demkov-Osherov model reformulated in terms of conventional scattering theory

Abstract

One of the few exactly solvable time-dependent quantum-mechanics problems was first analyzed by Demkov and Osherov 30 years ago {bold (}Zh. {acute E}ksp. Teor. Fiz. {bold 53}, 1589 (1967) [Sov. Phys. JETP {bold 26}, 916 (1968)]{bold )}. This model problem describes the interaction of a set of approximate stationary states with an additional state whose energy, in zeroth approximation, is a linear function of time. The Demkov-Osherov model is reexamined here using conventional Fourier transform methods. Emphasis on forward propagation in time eliminates the need for a Laplace transform of the wave function, as well as the resultant choice of contours for the evaluation of transition amplitudes. The evolution operator for the model Hamiltonian is expressed in terms of a single, frequency-dependent Sturmian. Such Sturmian functions are of considerable current interest in the analysis of nonadiabatic phenomena. {copyright} {ital 1998} {ital The American Physical Society}