## Abstract

The one-dimensional harmonic oscillator wave functions are solutions to a Sturm-Liouville problem posed on the whole real line. This problem generates the Hermite polynomials. However, no other set of orthogonal polynomials can be obtained from a Sturm-Liouville problem on the whole real line. In this paper it is shown how to characterize an arbitrary set of polynomials orthogonal on ( -∞,∞) in terms of a system of integrodifferential equations of the Hartree-Fock type. This system replaces and generalizes the linear differential equation associated with a Sturm-Liouville problem. Our results are demonstrated for the special case of continuous Hahn polynomials.

Original language | English |
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Pages (from-to) | 3106-3125 |

Number of pages | 20 |

Journal | Journal of Mathematical Physics |

Volume | 36 |

Issue number | 6 |

DOIs | |

State | Published - 1995 |

Externally published | Yes |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics