We prove that the spectrum of a Schrödinger operator with a potential which is periodic in certain directions and super-exponentially decaying in the others is purely absolutely continuous. Therefore, we reduce the operator using the Bloch-Floquet-Gelfand transform in the periodic variables, and show that, except for at most a set of quasi-momenta of measure zero, the reduced operators satisfies a limiting absorption principle.

Original languageEnglish
Pages (from-to)107-121
Number of pages15
JournalDocumenta Mathematica
Volume9
Issue number1
StatePublished - 1 Dec 2004

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  • Mathematics(all)

ID: 51315052