Complex Trajectories in the Quartic Oscillator and Its Semiclassical Coherent-State Propagator

Abstract

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 caseV(q)=λq2/2+βq4and compare the results with an “exact” calculation.