Completeness relation for energy-dependent separable potentials

Research output: Contribution to journalArticle

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. © 1985 American Institute of Physics.
Original languageAmerican English
Pages (from-to)1380-1386
Number of pages1241
JournalJournal of Mathematical Physics
DOIs
StatePublished - 1 Jan 1985

Fingerprint

Physics
completeness
Eigenfunctions
Completeness
eigenvectors
Dependent
Energy
Three-body Problem
three body problem
Conserve
energy
theorems
Linearly
physics
Necessary
Theorem

Cite this

@article{539cc371e2a7424494a7e00a77aa4be5,
title = "Completeness relation for energy-dependent separable potentials",
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. {\circledC} 1985 American Institute of Physics.",
author = "Humberto Garcilazo",
year = "1985",
month = "1",
day = "1",
doi = "10.1063/1.526950",
language = "American English",
pages = "1380--1386",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics",

}

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

In: Journal of Mathematical Physics, 01.01.1985, p. 1380-1386.

Research output: Contribution to journalArticle

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.

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=36549090615&origin=inward

UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=36549090615&origin=inward

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 -