Abstract:
We consider the one-dimensional Schrödinger equation 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.
Author information
Authors and Affiliations
Additional information
Received: 19 June 1996 / Accepted: 11 September 1996
Rights and permissions
About this article
Cite this article
Remling, C. A Probabilistic Approach to One-Dimensional Schrödinger Operators with Sparse Potentials . Comm Math Phys 185, 313–323 (1997). https://doi.org/10.1007/s002200050092
Issue Date:
DOI: https://doi.org/10.1007/s002200050092