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Zbl 0677.34026
Jensen, Arne
Scattering theory for Hamiltonians with Stark effect. (English)
[J] Ann. Inst. Henri Poincaré, Phys. Théor. 46, 383-395 (1987). ISSN 0246-0211

The spectrum problem of Hamiltonians with Stark effect attracted recently a considerable interest of many authors, for example, {\it F. Delyon, B. Simon} and {\it 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 $$ W\sb{\pm}(H,H\sb 0)=-\lim\sb{t\to \pm \infty}e\sp{it H} e\sp{-it H\sb 0} $$ exist and are asymptotically complete under some assumptions on H, $H\sb 0$.
[J.Tian]

MSC 2000:: *34L99 Ordinary differential operators

Keywords: selfadjoint operator; symmetric operator; Schrödinger operator; scattering theory; Hamiltonians with Stark effect; wave operators

Citations: Zbl 0579.60056; Zbl 0606.34020; Zbl 0608.35013

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