Semiclassical propagation of coherent states using complex and real trajectories (10 pages)

Marcel Novaes

Andrew E. Rubin

Andrew E. Rubin, John R. Klauder

Marcel Novaes

The semiclassical approximation to the coherent state propagator requires complex classical trajectories in order to satisfy the associated boundary conditions, but finding these trajectories in practice is a difficult task that may compromise the applicability of the approximation. In this work several approximations to the coherent state propagator are derived that make use only of real trajectories, which are easier to handle and have a more direct physical interpretation. It is verified in a particular example that these real trajectories approximations may have excellent accuracy.

Ademir Luiz Xavier Junior, Marcus A. M. de Aguiar

We compute the semiclassical coherent-state propagator for a particle moving in a one-dimensional box. In this semiclassical approach complex trajectories are stationary paths of the propagator's asymptotic expansion and play a fundamental role. A second semiclassical approximation is also introduced, which makes use of real trajectories only. An application to a seemingly simple system, the infinite well, is carried out completely for the diagonal elements, and a comparison is made among the three possible methods, those based on complex and real trajectories and the ``exact case'' that is determined by decomposing the propagator into its eigenstates. \textcopyright{} 1996 The American Physical Society.

George A. Hagedorn