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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
Posted:
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
- 1.
M. Ashbaugh and R. Benguria, Optimal lower bound for the gap between the first two eigenvalues of one-dimensional Schrödinger operators with symmetric single-well potentials, Proc. Amer. Math. Soc. (1989), 105 419-424. MR 0942630 (89f:81028)
- 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, Muegyetem 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, Muegyetem 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
Posted:
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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