Completeness relation for energy-dependent separable potentials

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Resumen

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.

Idioma originalInglés
Páginas (desde-hasta)1380-1386
Número de páginas7
PublicaciónJournal of Mathematical Physics
Volumen26
N.º6
DOI
EstadoPublicada - 1985

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