Semi-classical propagation of wavepackets for the phase space Schrödinger equation: interpretation in terms of the Feichtinger algebra

Abstract

The nearby orbit method is a powerful tool for constructing semi-classical solutions of Schrödinger's equation when the initial datum is a coherent state. In this paper, we first extend this method to arbitrary squeezed states and thereafter apply our results to the Schrödinger equation in phase space. This adaptation requires the phase-space Weyl calculus developed in previous work of ours. We also study the regularity of the semi-classical solutions from the point of view of the Feichtinger algebra familiar from the theory of modulation spaces.