Reducibility of relativistic Schr\"odinger equation with unbounded perturbations

TL;DR

This paper proves that a relativistic Schr"odinger equation with certain unbounded perturbations can be simplified to a time-independent form, aiding in understanding its long-term behavior.

Contribution

It establishes a reducibility result for a relativistic Schr"odinger equation with unbounded perturbations of order 1/2, transforming it into a block diagonal form.

Findings

Successfully conjugated the original equation to a time-independent form

Extended reducibility techniques to unbounded perturbations of order 1/2

Provided a framework for analyzing long-term dynamics of relativistic quantum systems

Abstract

In this paper, we prove a reducibility result for a relativistic Schr\"odinger equation on torus with time quasi-periodic unbounded perturbations of order 1/2, and finally conjugate the original equation to a time independent, 2\times 2 block diagonal one.