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

Published online by Cambridge University Press:  25 March 2009

Min-Jei Huang  and
Tzong-Mo Tsai
Min-Jei Huang
Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu 30043, Taiwan ([email protected])
Tzong-Mo Tsai
Affiliation:
Department of Electrical Engineering, Mingchi University of Technology, Taishan, Taipei 24301, Taiwan
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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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 2 , April 2009 , pp. 359 - 366
Copyright
Copyright © Royal Society of Edinburgh 2009

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