### 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 R^{n}, 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 |
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Pages (from-to) | 2325-2332 |

Number of pages | 8 |

Journal | Journal of Mathematical Physics |

Volume | 39 |

Issue number | 4 |

Publication status | Published - Apr 1998 |

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### ASJC Scopus subject areas

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

### Cite this

**Extremal eigenvalue gaps for the Schrödinger operator with Dirichlet boundary conditions.** / Karaa, Samir.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 39, no. 4, pp. 2325-2332.

}

TY - JOUR

T1 - Extremal eigenvalue gaps for the Schrödinger operator with Dirichlet boundary conditions

AU - Karaa, Samir

PY - 1998/4

Y1 - 1998/4

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0032397771&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032397771&partnerID=8YFLogxK

M3 - Article

VL - 39

SP - 2325

EP - 2332

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 4

ER -