An Estimate of the Gap of the First Two Eigenvalues in the Schr
An Estimate of the Gap of the First Two Eigenvalues in the Schr
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发表时间：
2009-02
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通讯作者：
S. Yau
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作者：
S. Yau
在势是强凸的情况下，给出了Schrodinger算子前两个本征值的差距的一个较低的估计。特别地，如果势函数的海森函数由正的常数从下向上限定，则差距具有与维数无关的下限。当势不一定是凸势时，我们也估计了差距。
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.