### Abstract

Original language | American English |
---|---|

Pages (from-to) | 1380-1386 |

Number of pages | 1241 |

Journal | Journal of Mathematical Physics |

DOIs | |

State | Published - 1 Jan 1985 |

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**Completeness relation for energy-dependent separable potentials.** / Garcilazo, Humberto.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Completeness relation for energy-dependent separable potentials

AU - Garcilazo, Humberto

PY - 1985/1/1

Y1 - 1985/1/1

N2 - We point out that the eigenfunctions of energy-dependent separable potentials, which are commonly used in the relativistic three-body problem, form a complete set of states. The completeness property is important, since it is necessary in order to satisfy the optical theorem, and consequently to conserve probability. We show that there exists a large family of energy-dependent separable potentials whose eigenfunctions form a complete set. Although the eigenfunctions of these potentials are not mutually orthogonal, it is shown that in general they are linearly independent. © 1985 American Institute of Physics.

AB - We point out that the eigenfunctions of energy-dependent separable potentials, which are commonly used in the relativistic three-body problem, form a complete set of states. The completeness property is important, since it is necessary in order to satisfy the optical theorem, and consequently to conserve probability. We show that there exists a large family of energy-dependent separable potentials whose eigenfunctions form a complete set. Although the eigenfunctions of these potentials are not mutually orthogonal, it is shown that in general they are linearly independent. © 1985 American Institute of Physics.

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U2 - 10.1063/1.526950

DO - 10.1063/1.526950

M3 - Article

SP - 1380

EP - 1386

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

ER -