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arXiv · 1711.07556

Asymptotic Completeness and S-Matrix for Singular Perturbations

Andrea Mantile·Andrea Posilicano
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Abstract

We give a criterion of asymptotic completeness and provide a representation of the scattering matrix for the scattering couple $(A_{0},A)$, where $A_{0}$ and $A$ are semi-bounded self-adjoint operators in $L^{2}(M,{\mathscr B},m)$ such that the set $\{u\in D(A_{0})\cap D(A):A_{0}u=Au\}$ is dense. No sort of trace-class condition on resolvent differences is required. Applications to the case in which $A_{0}$ corresponds to the free Laplacian in $L^{2}({\mathbb R}^{n})$ and $A$ describes the Laplacian with self-adjoint boundary conditions on rough compact hypersurfaces are given.

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Andrea Mantile, Andrea Posilicano. 2017-11-20. Asymptotic Completeness and S-Matrix for Singular Perturbations. https://doi.org/10.1016/j.matpur.2019.01.017

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