New Estimates for a Time-Dependent Schroedinger Equation

TL;DR

This paper introduces new mathematical estimates for the Schrödinger equation with time-dependent potentials, advancing understanding in quantum mechanics and PDE analysis, including novel results even for static potentials.

Contribution

It develops new estimates for linear Schrödinger equations with time-dependent potentials, utilizing a novel approach based on an abstract Wiener's Theorem, applicable in critical function spaces.

Findings

New estimates for time-dependent Schrödinger equations in R^3

Results extend to time-independent cases with novel methods

Applicable to scaling-critical, translation-invariant potential spaces

Abstract

This paper establishes new estimates for linear Schroedinger equations in R^3 with time-dependent potentials. Some of the results are new even in the time-independent case and all are shown to hold for potentials in scaling-critical, translation-invariant spaces. The proof of the time-independent results uses a novel method based on an abstract version of Wiener's Theorem.