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Scattering theory for Hamiltonians with Stark effect. (English) Zbl 0677.34026

The spectrum problem of Hamiltonians with Stark effect attracted recently a considerable interest of many authors, for example, F. Delyon, B. Simon and B. Souillard [Ann. Inst. Henri Poincaré, Phys. Theor. 42, 283-309 (1985; Zbl 0579.60056)]. Many of the known results were obtained in one dimension. Thus it is of interest to study the wave operator in dimension \(n>1\) and to include a large class of potentials. This paper is a sequel of the previous work of the author [Commun. Math. Phys. 107, 21-28 (1986; Zbl 0606.34020); Lect. Notes Math. 1218, 151-166 (1986; Zbl 0608.35013)]. The main result of this paper is that the wave operators \[ W_{\pm}(H,H_ 0)=-\lim_{t\to \pm \infty}e^{it H} e^{-it H_ 0} \] exist and are asymptotically complete under some assumptions on H, \(H_ 0\).
Reviewer: J.Tian

MSC:

34L99 Ordinary differential operators
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References:

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