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Title: On the Completeness Problem for the Eigenfunction Formulae of Relativistic Quantum Mechanics

Abstract

Dirac's theory of relativistic quantum mechanics leads to the problem of solving a set of four partial differential equations for the four components of the wave function. Solutions of these equations in the case where the potential is a function of the radial co-ordinate only were obtained by Darwin. It is proved that these solutions form a complete set in the sense that we can simultaneously expand four arbitrary functions in terms of them.

Authors:
Publication Date:
Research Org.:
Originating Research Org. not identified
Sponsoring Org.:
USDOE
OSTI Identifier:
4841572
NSA Number:
NSA-15-028225
Resource Type:
Journal Article
Journal Name:
Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences
Additional Journal Information:
Journal Volume: 262; Journal Issue: 1311; Other Information: Orig. Receipt Date: 31-DEC-61; Journal ID: ISSN 1364-5021
Publisher:
The Royal Society Publishing
Country of Publication:
Country unknown/Code not available
Language:
English
Subject:
PHYSICS; DIFFERENTIAL EQUATIONS; DIRAC EQUATIONS; EIGENFUNCTIONS; ELECTRIC POTENTIAL; EQUATIONS; MATHEMATICS; QUANTUM MECHANICS; RELATIVITY THEORY; WAVE MECHANICS

Citation Formats

Titchmarsh, E. C. On the Completeness Problem for the Eigenfunction Formulae of Relativistic Quantum Mechanics. Country unknown/Code not available: N. p., 1961. Web. doi:10.1098/rspa.1961.0134.
Titchmarsh, E. C. On the Completeness Problem for the Eigenfunction Formulae of Relativistic Quantum Mechanics. Country unknown/Code not available. doi:10.1098/rspa.1961.0134.
Titchmarsh, E. C. Tue . "On the Completeness Problem for the Eigenfunction Formulae of Relativistic Quantum Mechanics". Country unknown/Code not available. doi:10.1098/rspa.1961.0134.
@article{osti_4841572,
title = {On the Completeness Problem for the Eigenfunction Formulae of Relativistic Quantum Mechanics},
author = {Titchmarsh, E. C.},
abstractNote = {Dirac's theory of relativistic quantum mechanics leads to the problem of solving a set of four partial differential equations for the four components of the wave function. Solutions of these equations in the case where the potential is a function of the radial co-ordinate only were obtained by Darwin. It is proved that these solutions form a complete set in the sense that we can simultaneously expand four arbitrary functions in terms of them.},
doi = {10.1098/rspa.1961.0134},
journal = {Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences},
issn = {1364-5021},
number = 1311,
volume = 262,
place = {Country unknown/Code not available},
year = {1961},
month = {8}
}