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

TL;DR

This paper proves that certain 1D Schrödinger equations with unbounded, quasiperiodic perturbations can be simplified to a more manageable form, extending reducibility results to broader classes of potentials.

Contribution

It establishes reducibility for 1D Schrödinger equations with unbounded quasiperiodic perturbations, including magnetic and smooth potentials, broadening previous results.

Findings

System is reducible under specified conditions.

Includes unbounded symbols with controlled growth.

Extends reducibility to magnetic and smooth potentials.

Abstract

We study the Schr\"odinger equation on $\R$ with a potential behaving as $x^{2l}$ at infinity, $l\in[1,+\infty)$ and with a small time quasiperiodic perturbation. We prove that, if the perturbation belongs to a class of unbounded symbols including smooth potentials and magnetic type terms with controlled growth at infinity, then the system is reducible.