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

Shing-Tung Yau

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arXiv · 0902.2250

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

Shing-Tung Yau

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Abstract

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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Shing-Tung Yau. 2009-02-13. An Estimate of the Gap of the First Two Eigenvalues in the Schrödinger Operator. https://arxiv.org/abs/0902.2250

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