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Long-Range Scattering for Discrete Schrödinger Operators

  • Yukihide TadanoEmail author
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Abstract

In this paper, we define time-independent modifiers to construct a long-range scattering theory for a class of difference operators on \(\mathbb {Z}^d\), including the discrete Schrödinger operators on the square lattice. The modifiers are constructed by observing the corresponding Hamilton flow on \(T^*\mathbb {T}^d\). We prove the existence and completeness of modified wave operators in terms of the above-mentioned time-independent modifiers.

Mathematics Subject Classification

47A40 47B39 81U05 

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Notes

Acknowledgements

The author would like to thank Professor Shu Nakamura, my Ph.D. advisor. This paper would not be completed without his advice. The author is also grateful to Professor Hiroshi Isozaki for his kind discussion.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesThe University of TokyoTokyoJapan

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