# 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}

}

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