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

MathSciNet review:
875408

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Abstract: We prove the optimal upper bound 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.

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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