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 language | English |
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Pages (from-to) | 1380-1386 |
Number of pages | 7 |
Journal | Journal of Mathematical Physics |
Volume | 26 |
Issue number | 6 |
DOIs | |
State | Published - 1985 |