×

Schrödinger operators with sparse potentials: asymptotics of the Fourier transform of the spectral measure. (English) Zbl 1161.81378

Summary: We study the pointwise behavior of the Fourier transform of the spectral measure for discrete one-dimensional Schrödinger operators with sparse potentials. We find a resonance structure which admits a physical interpretation in terms of a simple quasiclassical model. We also present an improved version of known results on the spectrum of such operators.

MSC:

81Q99 General mathematical topics and methods in quantum theory
35Q40 PDEs in connection with quantum mechanics
47B39 Linear difference operators
47N50 Applications of operator theory in the physical sciences
PDFBibTeX XMLCite
Full Text: DOI