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

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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.
Published version of the 2003 article for the Proceedings in honor of Louis Nirenberg's 75th birthday, Hsinchu, Sept. 2000

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Differential Geometry, Analysis of PDEs

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http://salesiana.dossiersoluciones.com/handle/123456789/219811

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0902.2250
 http://arxiv.org/abs/0902.2250
 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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arXiv