02-149 I. Herbst, E. Skibsted
Quantum scattering for potentials independent of |x|: Asymptotic completeness for high and low energies (647K, Postscript) Mar 26, 02
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Abstract. Let $V_1: S^{n-1} \rarrow \mathbb{R}$ 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 short-range 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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