An Estimate of the Gap of the first two Eigenvalues in the Schrödinger Operator
نویسنده
چکیده
In my previous paper [2] with I. M. Singer, B. Wong and Stephen Yau, I gave a lower estimate of the gap of the first 2 eigenvalues of the Schrödinger operator in case the potential is convex. In this note we note that the estimate can be improved if we assume 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 dimension. We also find gap when the potential is not necessary convex.
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تاریخ انتشار 2003