### 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 |
---|---|

Pages (from-to) | 2325-2332 |

Number of pages | 8 |

Journal | Journal of Mathematical Physics |

Volume | 39 |

Issue number | 4 |

Publication status | Published - Apr 1998 |

### Fingerprint

### ASJC Scopus subject areas

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