### Abstract

The authors prove a number of results asserting the existence of eigenvalues of the Schrödinger operator H-λW in a gap of σ(H), where H=-Δ+V and V and W are bounded. The existence of these eigenvalues is an important element in the theory of the colour of crystals. The basic theorems are proved in ℝ^{v}; stronger results for v=1 are also presented.

Original language | English (US) |
---|---|

Pages (from-to) | 461-490 |

Number of pages | 30 |

Journal | Communications In Mathematical Physics |

Volume | 103 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1986 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

## Fingerprint Dive into the research topics of 'On the existence of eigenvalues of the Schrödinger operator H-λW in a gap of σ(H)'. Together they form a unique fingerprint.

## Cite this

Deift, P. A., & Hempel, R. (1986). On the existence of eigenvalues of the Schrödinger operator H-λW in a gap of σ(H).

*Communications In Mathematical Physics*,*103*(3), 461-490. https://doi.org/10.1007/BF01211761