## Abstract

A class of second order difference (discrete) operators with a partial algebraization of the spectrum is introduced. The eigenfuncions of the algebraized part of the spectrum are polynoms (discrete polynoms). Such difference operators can be constructed by means of U_{q}(sl_{2}) the quantum deformation of the sl_{2} algebra. The roots of the polynoms determine the spectrum and obey the Bethe ansatz equations. A particular case of difference equations for q-hypergeometric and Askey-Wilson polynoms is discussed. Applications to the problem of Bloch electrons in a magnetic field are outlined.

Original language | English |
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Pages (from-to) | 699-724 |

Number of pages | 26 |

Journal | Nuclear Physics B |

Volume | 451 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2 Oct 1995 |

Externally published | Yes |

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