Completeness relation for energy-dependent separable potentials

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Abstract

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.

Original languageEnglish
Pages (from-to)1380-1386
Number of pages7
JournalJournal of Mathematical Physics
Volume26
Issue number6
DOIs
StatePublished - 1985

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