## 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 L^{2}(R^{n-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 = V_{script A sign} + V_{e}, where V_{script A sign} is analytic in a sector with V_{script A sign}(x) = O(〈x^{1}〉^{-1/2-ε}), and V_{e}(x) = O(e^{μx1}), for x_{1} < 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