The Scattering Matrix and its Meromorphic Continuation in the Stark Effect Case期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The Scattering Matrix and its Meromorphic Continuation in the Stark Effect Case

Authors:	Hislop P D White D A W

Institution:	(1) Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA;(2) Department of Mathematics, The University of Toledo, Toledo, OH, 43606-3390, U.S.A

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(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 $V = V_\mathcal{A} + V_e$ , where $V_\mathcal{A}$ is analytic in a sector with $V_\mathcal{A} (x) = O(\left\langle {x_{} } \right\rangle ^{ - 1/2 - \varepsilon } )$ , and $V_e (x) = O({\text{e}}^{\mu x_1 } )$ , for x₁<0 and some >0. These potentials include the Coulomb potential. The wave operators used to define the scattering matrix are the two Hilbert space wave operators.

Keywords:	scattering matrix stark continuation Schrö dinger
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