Extremal eigenvalue gaps for the Schrodinger operator with Dirichlet boundary conditions

We consider the problems of minimizing and maximizing the gap between the two lowest Dirichlet eigenvalues of the Schrodinger operator - Delta + V(x) on a bounded domain in R-n, when the potential V is subjected to a p-norm constraint. We give characterization theorems for extremizing potentials. We prove in particular that a second eigenvalue corresponding to a minimizing potential is always single. (C) 1998 American Institute of Physics. [S0022-2488(98)03903-6].