Abstract
Quantum scattering in the presence of a constant electric field ('Stark effect') is considered. It is shown that the scattering matrix has a meromorphic continuation in the energy variable to the entire complex plane as an operator on L2(Rn-1). The allowed potentials V form a general subclass of potentials that are short-range relative to the free Stark Hamiltonian: Roughly, the potential vanishes at infinity, and admits a decomposition V = Vscript A sign + Ve, where Vscript A sign is analytic in a sector with Vscript A sign(x) = O(〈x1〉-1/2-ε), and Ve(x) = O(eμx1), for x1 < 0 and some μ, ε > 0. These potentials include the Coulomb potential. The wave operators used to define the scattering matrix are the two Hilbert space wave operators.
Original language | English |
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Pages (from-to) | 201-209 |
Number of pages | 9 |
Journal | Letters in Mathematical Physics |
Volume | 48 |
Issue number | 3 |
DOIs | |
State | Published - May 1999 |
Bibliographical note
Funding Information:The first author’s research was supported in part by NSF grant DMS-9707049.
Keywords
- Schrödinger
- Stark,
- continuation
- scattering matrix
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics