Long range scattering with Stark effect and almost periodic potentials

Abstract

Spectral and scattering theory is discussed for the Stark effect Hamiltonians H0=−(1/2)Δ−x1 and H=H0+V where V is a long range perturbation. Most significantly, in one dimension, and for V consisting of a slowly decaying term and an almost periodic term, the two Hilbert space wave operators (of Isozaki and Kitada) are shown to exist and be complete by Enss's time dependent method.

Keywords

• long range scattering
• Stark effect
• almost periodic
• two Hilbert space wave operators.