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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

   
 

 

Some Schrödinger operators
with dense point spectrum


Author: Barry Simon
Journal: Proc. Amer. Math. Soc. 125 (1997), 203-208
MSC (1991): Primary 34L99, 81Q05
DOI: https://doi.org/10.1090/S0002-9939-97-03559-4
MathSciNet review: 1346989
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Abstract: Given any sequence $\{E_{n}\}^{\infty }_{n=1}$ of positive energies and any monotone function $g(r)$ on $(0,\infty )$ with $g(0)=1$, $\lim \limits _{r\to \infty } g(r)=\infty $, we can find a potential $V(x)$ on $(-\infty ,\infty )$ such that $\{E_{n}\}^{\infty }_{n=1}$ are eigenvalues of $-\frac {d^{2}}{dx^{2}}+V(x)$ and $|V(x)|\leq (|x|+1)^{-1}g(|x|)$.


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Additional Information

Barry Simon
Affiliation: Division of Physics, Mathematics, and Astronomy, California Institute of Technology, 253-37, Pasadena, California 91125
Email: bsimon@caltech.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03559-4
Received by editor(s): July 26, 1995
Additional Notes: This material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 Barry Simon