Reducibility of 1-d Schr\"odinger equation with unbounded time quasiperiodic perturbations, III

TL;DR

This paper advances the understanding of transforming 1D quantum harmonic and anharmonic oscillators with unbounded quasiperiodic time-dependent perturbations into simpler forms, extending previous reducibility results.

Contribution

It introduces modified algorithms that handle larger perturbations than those addressed in prior research, improving reducibility techniques for quantum oscillators.

Findings

Successfully extends reducibility to higher-order perturbations

Develops new algorithmic approach for unbounded quasiperiodic perturbations

Enhances theoretical framework for quantum oscillator analysis

Abstract

In this paper we study reducibility of time quasiperiodic perturbations of the quantum harmonic or anharmonic oscillator in one space dimension. We modify known algorithms obtaining a reducibility result which allows to deal with perturbations of order strictly larger than the ones considered in all the previous papers.