The comparative roles of connected and disconnected trajectories in the evaluation of the semiclassical coherent-state propagator

Andrew E. Rubin, John R. Klauder

Marcel Novaes, Marcus A. M. de Aguiar

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.

Satoshi Adachi

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

The semiclassical approximation of the coherent-state propagator requires the computation of complex trajectories satisfying special boundary conditions. In this paper we present a method for the determination of such trajectories for one-dimensional polynomial potentials. We also compute the semiclassical propagator for the case V ( q )= λq 2 /2+ βq 4 and compare the results with an “exact” calculation.