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Published 2011 | Published
Book Section - Chapter Open

Schrödinger operators with potential V(n)=N^(-y) cos (2πn^p)

Abstract

Let H be the Schrödinger operator with potential V(n) = n^(−γ) cos(2πn^ρ), where ρ ∈ (1,2) and γ ∈ (0, 1/2 − ρ−1/2). I show that for almost every boundary condition H has pure-point spectrum.

Additional Information

© 2011 American Mathematical Society. I am thanking to Daniel Ueltschi and Robert Sims for their kind invitation to the second Arizona School of Analysis with Applications, where the idea for this project originated. Furthermore, I thank Milivoje Lukic for useful discussions. I also like to thank Günter Stolz for useful discussions, which lead to the choice of (1.7). This work was done while H. K. was an Erwin Schrödinger Junior Research Fellow. Parts of this work are supported by a fellowship of the Simons Foundation.

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