The phase delay and its complex time: From stationary states up to wave packets

Abstract

Complex time is often invoked about tunneling effect where the classical phase delay is completed with a crucial filter effect. Usually the complex times are obtained by considering the flux–flux correlation function, but this can be obtained by a very simple approach using the search of the maximum of the generalized complex phase function, including the amplitude of the wave function. Various aspects of the phase delay are presented in the case of wave packets impinging on simple or resonant quantum barriers.Formal links with the classical mechanics give birth to quasi-trajectories of the quantum particle, totally compatible with the quantum mechanics.