ON SHARP LOWER BOUND OF THE GAP FOR THE FIRST TWO EIGENVALUES IN THE SCHRÖDINGER OPERATOR

Abstract

[8] is a deep study in the sharp lower bound estimate of the gap for the first two eigenvalues in Schr\{o}dinger operator on a smooth bounded convex domain in $\mathbb{R}^n$. In this paper we give another simple proof of the main result in [8]. Although the methods used in here due to [8] on the whole, to some extent we deal with the singularity of some function and also simplify greatly calculation in [8].