The absolutely continuous spectrum of one-dimensional Schrodinger operators with decaying potentials

Autor(en): Remling, C
Stichwörter: HAMILTONIANS; Physics; Physics, Mathematical; POINT; VONNEUMANN WIGNER POTENTIALS
Erscheinungsdatum: 1998
Herausgeber: SPRINGER VERLAG
Journal: COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volumen: 193
Ausgabe: 1
Startseite: 151
Seitenende: 170
Zusammenfassung: 
We investigate one-dimensional Schrodinger operators with asymptotically small potentials. It will follow from our results that if V(x) less than or equal to C(1+x)(-alpha) with alpha > 1/2, then Sigma(ac) = (0, infinity) is an essential support of the absolutely continuous part of the spectral measure. We also prove that if C := lim sup(x-->infinity) xV(x) < infinity, then the spectrum is purely absolutely continuous on ((2C/pi)(2), infinity). These results are optimal.
ISSN: 00103616
DOI: 10.1007/s002200050322

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