Discrete and embedded eigenvalues for one-dimensional Schr"odinger operators

Details Discrete and embedded eigenvalues for one-dimensional Schr"odinger operators Discrete and embedded eigenvalues for one-dimensional Schr"odinger operators

2006-06-12

arxiv.org/abs/math/0606286v1

Mathematics

Spectral Theory

Scientific paper

I present an example of a discrete Schr"odinger 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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