Construction of Floquet–Bloch Solutions and Estimation of Lengths of Resonance Zones of One-Dimensional Schrödinger Equation with Smooth Potential

  • O. M. Denysenko
  • I. O. Parasyuk

Abstract

A one-dimensional Schrödinger equation with a potential characterized by a certain rate of approximation by trigonometric polynomials is investigated by methods of the KAM theory. Estimates for resonance energy zones are obtained. The case where the potential belongs to the Gevrey class is analyzed.
Published
25.01.2004
How to Cite
DenysenkoO. M., and ParasyukI. O. “Construction of Floquet–Bloch Solutions and Estimation of Lengths of Resonance Zones of One-Dimensional Schrödinger Equation With Smooth Potential”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, no. 1, Jan. 2004, pp. 3-18, https://umj.imath.kiev.ua/index.php/umj/article/view/3724.
Section
Research articles