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

Ashbaugh, Mark S.; Benguria, Rafael

doi:10.1090/S0002-9939-1987-0875408-4

Best constant for the ratio of the first two eigenvalues of one-dimensional Schrödinger operators with positive potentials
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by Mark S. Ashbaugh and Rafael Benguria

Proc. Amer. Math. Soc. 99 (1987), 598-599

DOI: https://doi.org/10.1090/S0002-9939-1987-0875408-4

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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.

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