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arXiv 0902.2250math.DGmath.AP
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薛定谔算子前两个本征值间隔的估计

An Estimate of the Gap of the First Two Eigenvalues in the Schrödinger Operator

Shing-Tung Yau

备注：
Published version of the 2003 article for the Proceedings in honor of Louis Nirenberg's 75th birthday, Hsinchu, Sept. 2000
发表信息：
Lectures on Partial Differential Equations. Edited by S.-Y. A. Chang, C.-S. Lin and H.-T. Yau. 223-235, New Stud. Adv. Math., 2, Int. Press, Somerville, MA, 2003
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摘要：

在势为强凸的情形下，给出了薛定谔算子前两个本征值的间隙的一个较低的估计。特别地，如果势函数的海森函数由正的常数从下向上限定，则间隙具有与维数无关的下界。我们还估计的差距时，潜在的不一定是凸的。

英文摘要：

We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator in the case when the potential is strongly convex. In particular, if the Hessian of the potential is bounded from below by a positive constant, the gap has a lower bound independent of the dimension. We also estimate the gap when the potential is not necessarily convex.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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