 02149 I. Herbst, E. Skibsted
 Quantum scattering for potentials independent of x: Asymptotic
completeness for high and low energies
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Mar 26, 02

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Abstract. Let $V_1: S^{n1} \rarrow \mathbb{R}$ be a Morse function and define
$V_0(x) = V_1(x/x)$. We consider the scattering theory of the
Hamiltonian $H =  \frac{1}{2} \Delta + V(x)$ in $L^2(\mathbb{R}^n)$,
$n \geq 2$, where $V$ is a shortrange perturbation of $V_0$. We
introduce two types of wave operators for channels corresponding to
local minima of $V_1$ and prove completeness of these wave operators
in the appropriate energy ranges.
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