Extremal eigenvalue gaps for the Schrödinger operator with Dirichlet boundary conditions

Samir Karaa

doi:10.1063/1.532290

Extremal eigenvalue gaps for the Schrödinger operator with Dirichlet boundary conditions

Samir Karaa^*

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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 language	English
Pages (from-to)	2325-2332
Number of pages	8
Journal	Journal of Mathematical Physics
Volume	39
Issue number	4
DOIs	https://doi.org/10.1063/1.532290
Publication status	Published - Apr 1998

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "We consider the problems of minimizing and maximizing the gap between the two lowest Dirichlet eigenvalues of the Schr{\"o}dinger 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.",

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AB - 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.

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Extremal eigenvalue gaps for the Schrödinger operator with Dirichlet boundary conditions

Abstract

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