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 A comparison theorem of the eigenvalue gap for one-dimensional barrier potentials Bull. Korean Math. Soc. 2000 Vol. 37, No. 2, 353-360 Jung-Soon Hyun Yeungnam University Abstract : 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 Full-Text :