Scattering resonances as viscosity limits

Abstract

Using the method of complex scaling we show that scattering resonances of $- \Delta + V$, $V \in L^\infty_{\rm{c}} ( \mathbb R^n )$, are limits of eigenvalues of $- \Delta + V - i \epsilon x^2$ as $\epsilon \to 0+$. That justifies a method proposed in computational chemistry and reflects a general principle for resonances in other settings.Comment: 19 pages, 3 figure