Remarks on Scattering Matrices for Schrodinger Operators with Critically Long-Range Perturbations

Nakamura Shu

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Remarks on Scattering Matrices for Schrodinger Operators with Critically Long-Range Perturbations

机译：关于Schrodinger运算符的散射矩阵，具有批判性远程扰动

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We consider scattering matrix for Schrodinger-type operators on R-d with perturbation V (x) = O(< x >(-1)) as vertical bar x vertical bar -> infinity. We show that the scattering matrix (with time-independent modifiers) is a pseudodifferential operator and analyze its spectrum. We present examples of which the spectrum of the scattering matrices has dense point spectrum, and absolutely continuous spectrum, respectively. These give a partial answer to an open question posed by Yafaev (Scattering theory: some old and new problems. Springer Lecture Notes in Mathematical, vol 1735, 2000).

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来源
《Annales Henri Poincare》 |2020年第10期|共21页
作者
Nakamura Shu;
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作者单位

Gakushuin Univ Dept Math Toshima Ku 1-5-1 Mejiro Tokyo 1718588 Japan;

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正文语种 eng
中图分类理论物理学;
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Remarks on Scattering Matrices for Schrodinger Operators with Critically Long-Range Perturbations

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