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Abstract: We give a lower estimate of the gap of the first two eigenvalues of theSchrodinger operator in the case when the potential is strongly convex. Inparticular, if the Hessian of the potential is bounded from below by a positiveconstant, the gap has a lower bound independent of the dimension. We alsoestimate the gap when the potential is not necessarily convex.



Author: Shing-Tung Yau

Source: https://arxiv.org/



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