Estimates on modulation spaces for Schr\"{o}dinger operators with time-dependent sub-linear vector potentials

TL;DR

This paper provides estimates for solutions to the Schrödinger equation with time-dependent, sub-linear vector potentials within modulation spaces, advancing understanding of their behavior in quantum mechanics.

Contribution

It introduces new estimates for Schrödinger operators with sub-linear, time-dependent vector potentials in modulation spaces, a novel analysis in this context.

Findings

Solutions are bounded in modulation spaces under sub-linear vector potentials.

The estimates improve understanding of Schrödinger dynamics with time-dependent potentials.

Results extend previous work on Schrödinger operators to more general vector potentials.

Abstract

In this paper, we give estimates of the solutions to Schr\"{o}dinger equation on modulation spaces with vector potential of sub-linear growth.