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.
|Number of pages||9|
|Journal||Letters in Mathematical Physics|
|State||Published - May 1999|
Bibliographical noteFunding Information:
The first author’s research was supported in part by NSF grant DMS-9707049.
- scattering matrix
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics