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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A bound for ratios of eigenvalues of Schrödinger operators with single-well potentials


Authors: Miklós Horváth and Márton Kiss
Journal: Proc. Amer. Math. Soc. 134 (2006), 1425-1434
MSC (2000): Primary 34L15, 34B24
Published electronically: October 13, 2005
MathSciNet review: 2199189
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Abstract: For Schrödinger operators with nonnegative single-well potentials ratios of eigenvalues are extremal only in the case of zero potential. To prove this, we investigate some monotonicity properties of Prüfer-type variables.


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Additional Information

Miklós Horváth
Affiliation: Department of Mathematical Analysis, Institute of Mathematics, Budapest University of Technology and Economics, H 1111 Budapest, Műegyetem rkp. 3-9, Hungary
Email: horvath@math.bme.hu

Márton Kiss
Affiliation: Department of Mathematical Analysis, Institute of Mathematics, Budapest University of Technology and Economics, H 1111 Budapest, Műegyetem rkp. 3-9, Hungary
Email: mkiss@math.bme.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08100-1
PII: S 0002-9939(05)08100-1
Keywords: Schr\"odinger operator, eigenvalues.
Received by editor(s): December 5, 2003
Received by editor(s) in revised form: December 10, 2004, and December 14, 2004
Published electronically: October 13, 2005
Additional Notes: This research was supported by the Hungarian NSF Grants OTKA T 32374, T 37491 and T 47035
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2005 American Mathematical Society