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Best constant for the ratio of the first two eigenvalues of one-dimensional Schrödinger operators with positive potentials


Authors: Mark S. Ashbaugh and Rafael Benguria
Journal: Proc. Amer. Math. Soc. 99 (1987), 598-599
MSC: Primary 34B25
DOI: https://doi.org/10.1090/S0002-9939-1987-0875408-4
MathSciNet review: 875408
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Abstract: We prove the optimal upper bound $ {\lambda _2}/{\lambda _1} \leq 4$ for the ratio of the first two eigenvalues of one-dimensional Schrödinger operators with nonnegative potentials. Equality holds if and only if the potential vanishes identically.


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

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0875408-4
Keywords: Schrödinger operators, ratios of eigenvalues, commutation formula
Article copyright: © Copyright 1987 American Mathematical Society

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