Extremal eigenvalue gaps for the Schrödinger operator with Dirichlet boundary conditions

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Abstract

We consider the problems of minimizing and maximizing the gap between the two lowest Dirichlet eigenvalues of the Schrödinger operator -Δ + V(x) on a bounded domain in Rn, when the potential V is subjected to a p-norm constraint. We give characterization theorems for extrenming potentials. We prove in particular that a second eigenvalue corresponding to a minimizing potential is always single.

Original languageEnglish
Pages (from-to)2325-2332
Number of pages8
JournalJournal of Mathematical Physics
Volume39
Issue number4
Publication statusPublished - Apr 1998

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ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

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