### Abstract

We prove that the Schrödinger operator H=-d^{2}/dx^{2}+V(x)+F·x has purely absolutely continuous spectrum for arbitrary constant external field F, for a large class of potentials; this result applies to many periodic, almost periodic and random potentials and in particular to random wells of independent depth for which we prove that when F=0, the spectrum is almost surely pure point with exponentially decaying eigenfunctions.

Original language | English (US) |
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Pages (from-to) | 387-397 |

Number of pages | 11 |

Journal | Communications In Mathematical Physics |

Volume | 88 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1983 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Bentosela, F., Carmona, R., Duclos, P., Simon, B., Souillard, B., & Weder, R. (1983). Schrödinger operators with an electric field and random or deterministic potentials.

*Communications In Mathematical Physics*,*88*(3), 387-397. https://doi.org/10.1007/BF01213215