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Discrete and Embedded Eigenvalues for One-Dimensional Schrödinger Operators

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Abstract

I present an example of a discrete Schrödinger operator that shows that it is possible to have embedded singular spectrum and, at the same time, discrete eigenvalues that approach the edges of the essential spectrum (much) faster than exponentially. This settles a conjecture of Simon (in the negative). The potential is of von Neumann-Wigner type, with careful navigation around a previously identified borderline situation.

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  1. Mathematics Department, University of Oklahoma, Norman, OK, 73019-0315, USA

    Christian Remling

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  1. Christian Remling
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Correspondence to Christian Remling.

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Communicated by B. Simon

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Remling, C. Discrete and Embedded Eigenvalues for One-Dimensional Schrödinger Operators. Commun. Math. Phys. 271, 275–287 (2007). https://doi.org/10.1007/s00220-006-0185-z

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  • DOI: https://doi.org/10.1007/s00220-006-0185-z

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