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

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

2009-02-13

arxiv.org/abs/0902.2250v1

Lectures on Partial Differential Equations. Edited by S.-Y. A. Chang, C.-S. Lin and H.-T. Yau. 223-235, New Stud. Adv. Math.,

Mathematics

Differential Geometry

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

Scientific paper

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.

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