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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
DOI: https://doi.org/10.1090/S0002-9939-05-08100-1
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.


References [Enhancements On Off] (What's this?)

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  • 2. M. Ashbaugh and R. Benguria, Optimal bounds for ratios of eigenvalues of one-dimensional Schrödinger operators with Dirichlet boundary conditions and positive potentials, Commun. Math. Phys (1989), 124 403-415. MR 1012632 (91c:34114)
  • 3. B. M. Levitan and I. S. Sargsjan, Sturm-Liouville and Dirac operators (in Russian), Nauka, Moscow, (1988). MR 0958344 (90c:34028)

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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: https://doi.org/10.1090/S0002-9939-05-08100-1
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

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