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Scattering Resonances as Viscosity Limits

  • Maciej ZworskiEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 269)

Abstract

Using the method of complex scaling we show that scattering resonances of \( - \Delta + V \), \( V \in L^\infty _\mathrm{{c}} ( {\mathbb {R}}^n ) \), are limits of eigenvalues of \( - \Delta + V - i \varepsilon x^2 \) as \( \varepsilon \rightarrow 0+\). That justifies a method proposed in computational chemistry and reflects a general principle for resonances in other settings.

Notes

Acknowledgements

The author would like to thank Mike Christ, Semyon Dyatlov, Jeff Galkowski, John Strain and Joe Viola for helpful discussions. I am also grateful to the anonymous referee for the careful reading of the first version and for the valuable comments. This project was supported in part by the National Science Foundation grant DMS-1201417.

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Copyright information

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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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