White, D. A. W. The Stark effect and long range scattering in two Hilbert spaces. (English) Zbl 0695.35144 Indiana Univ. Math. J. 39, No. 2, 517-546 (1990). Quantum mechanical scattering is considered in the presence of a constant electric field. The “free” Hamiltonian is \(-\Delta -x_ 1\) and the full Hamiltonian is a perturbation by a long range potential V: \[ D^{\alpha}V(x)=O(1+| x|)^{-| \alpha | /2+\epsilon}\quad for\quad all\quad multi-indices\quad \alpha, \] for some \(\epsilon >0\). (A short range potential can also be included.) It is shown that the two Hilbert space wave operators exist and are complete. The approach is by Enss’s method using Isozaki and Kitada’s “time independent modifiers”. Central to their approach is the construction of the “modifier” which requires approximating a solution of a certain partial differential equation. This approximation is done here by an iteration scheme which is unlike the approximation method of earlier works. Reviewer: D.A.W.White Cited in 10 Documents MSC: 35P25 Scattering theory for PDEs 35J10 Schrödinger operator, Schrödinger equation Keywords:long range potential; wave operators; complete; Enss’s method; Stark effect × Cite Format Result Cite Review PDF Full Text: DOI