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.