Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials

Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials

The aim of this paper is to extend a class of potentials for which the absolutely continuous spectrum of the corresponding multidimensional Schrodinger operator is essentially supported by [0, infinity). Our main theorem states that this property is preserved for slowly decaying potentials provided...

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Veröffentlicht in:Communications in mathematical physics 2005-02, Vol.253 (3), p.611
Hauptverfasser: Laptev, Ari, Naboko, S., Safronov, Oleg
Format: Artikel
Sprache:eng
Schlagworte:
hamiltonians
jacobi matrices
scattering
vonneumann wigner potentials
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Beschreibung
Zusammenfassung:The aim of this paper is to extend a class of potentials for which the absolutely continuous spectrum of the corresponding multidimensional Schrodinger operator is essentially supported by [0, infinity). Our main theorem states that this property is preserved for slowly decaying potentials provided that there are some oscillations with respect to one of the variables.
ISSN:1432-0916
0010-3616
DOI:10.1007/s00220-004-1157-9