We study the Schrödinger equation on R with a potential behaving as x2l at infinity, l∈ [ 1 , + ∞) 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.
Reducibility of 1-d Schrödinger Equation with Time Quasiperiodic Unbounded Perturbations, II / D. Bambusi. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 353:1(2017 Jul 01), pp. 353-378.
Reducibility of 1-d Schrödinger Equation with Time Quasiperiodic Unbounded Perturbations, II
D. Bambusi
2017
Abstract
We study the Schrödinger equation on R with a potential behaving as x2l at infinity, l∈ [ 1 , + ∞) 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.
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