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The gap between the first two eigenvalues of a one-dimensional Schrödinger operator with symmetric potential


Author: S. Abramovich
Journal: Proc. Amer. Math. Soc. 111 (1991), 451-453
MSC: Primary 34L40; Secondary 34B05, 34L15, 47E05, 81Q10
DOI: https://doi.org/10.1090/S0002-9939-1991-1036981-X
MathSciNet review: 1036981
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Abstract: We prove the inequality $ {\lambda _2}[{V_1}] - {\lambda _1}[{V_1}] \geq {\lambda _2}[{V_0}] - {\lambda _1}[{V_0}]$ for the difference of the first two eigenvalues of one-dimensional Schrödinger operators $ - \frac{{{d^2}}}{{d{x^2}}} + {V_i}(x),i = 0,1$, where $ {V_1}$ and $ {V_0}$ are symmetric potentials on $ (a,b)$ and on $ (a,(a + b)/2)$, and $ {V_0} - {V_1}$ is decreasing on $ (a,(3a + b)/4)$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1036981-X
Keywords: Schrödinger operators, eigenvalue gaps
Article copyright: © Copyright 1991 American Mathematical Society

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