Bulletin of the
Korean Mathematical Society BKMS

The fundamental gap between the lowest two Dirichlet eigenvalues for a Schr\"{o}dinger operator $H_R=-\frac{d^2}{dx^2}+V(x)$ on $L^2\left(\left[ -R,R\right]\right)$ is compared with the gap for a same operator $H_S$ with a different domain $\left[-S,S\right]$ and the difference is exponentially small when the potential has a large barrier.

Keywords: Schrodinger operator, eigenvalue gap

MSC numbers: 34L40