Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

The eigenvalue gap for one-dimensional Schrödinger operators with symmetric potentials

Min-Jei Huanga1 and Tzong-Mo Tsaia2

a1 Department of Mathematics, National Tsing Hua University, Hsinchu 30043, Taiwan (mjhuang@math.nthu.edu.tw)

a2 Department of Electrical Engineering, Mingchi University of Technology, Taishan, Taipei 24301, Taiwan

Abstract

We consider the eigenvalue gap for Schrödinger operators on an interval with Dirichlet or Neumann boundary conditions. For a class of symmetric potentials, we prove that the gap between the two lowest eigenvalues is maximized when the potential is constant. We also give some related results for doubly symmetric potentials.

(Received March 26 2007)

(Accepted March 06 2008)