Long range scattering with Stark effect and almost periodic potentials

Spectral and scattering theory is discussed for the Stark effect Hamiltonians H0= ￠ ’(1/2) ” ￠ ’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.