Singularities for solutions to time dependent Schr\"odingier equations with sub-quadratic potential

TL;DR

This paper characterizes the wave front sets of solutions to time-dependent Schrödinger equations with sub-quadratic potentials using wave packet transforms, advancing understanding of solution singularities.

Contribution

It introduces a method to determine wave front sets of Schrödinger solutions with sub-quadratic potentials via wave packet transform representation.

Findings

Wave front sets of solutions are explicitly characterized.

Wave packet transform effectively captures solution singularities.

Method applies to a class of Schrödinger equations with sub-quadratic potentials.

Abstract

In this article, we determine the wave front sets of solutions to time dependent Schr\"odinger equations with a sub-quadratic potential by using the representation of the Schr\"dingier evolution operator via wave packet transform (short time Fourier transform).