The scattering matrix and its meromorphic continuation in the Stark effect case

P. D. Hislop, D. A.W. White

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1 Scopus citations


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 languageEnglish
Pages (from-to)201-209
Number of pages9
JournalLetters in Mathematical Physics
Issue number3
StatePublished - May 1999

Bibliographical note

Funding Information:
The first author’s research was supported in part by NSF grant DMS-9707049.


  • Schrödinger
  • Stark,
  • continuation
  • scattering matrix

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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