A probabilistic approach to one-dimensional Schrodinger operators with sparse potentials

Autor(en): Remling, C
Stichwörter: Physics; Physics, Mathematical; SINGULAR CONTINUOUS-SPECTRUM
Erscheinungsdatum: 1997
Herausgeber: SPRINGER VERLAG
Journal: COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volumen: 185
Ausgabe: 2
Startseite: 313
Seitenende: 323
Zusammenfassung: 
We consider the one-dimensional Schrodinger equation -y `' Vy = Ey with sparse potential V (i.e. mainly V = 0). It is shown that the asymptotics of the solutions corresponding to positive energies E can be approximately described by an infinite sum of independent random variables. Using results from probability theory, we can then determine the spectral properties of the operators under consideration. We prove absolute continuity for a general class of potentials, and we also have examples with singular continuous spectrum.
ISSN: 00103616
DOI: 10.1007/s002200050092

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