Estimates on the Lower Bound of the First Gap

Abstract

We give a new lower bound for the first gap $\hat{I}{»}_2-\hat{I}{»}_1$ of the Dirichlet eigenvalues of the Schr{ö}dinger operator on a bounded convex domain $\hat{I}\text{c◯}$ in R${}^n$ or S${}^n$ and greatly sharpens the previous estimates. The new bound is explicit and computable.

enhanced results, 26 pages