# NORMALIZATION CONDITION FOR THE BETHE-SALPETER WAVE FUNCTION AND A FORMAL SOLUTION TO THE BETHE-SALPETER EQUATION

## Abstract

By the use of an inhomogeneous Bethe-Salpeter equation a normalization condition for the Bethe-Salpeter wave function is obtained. This condition requires the normalization integral to be positive. A formal solution is obtained in the ladder approximation, and convergence of the normalization integral is proved by the use of this solution. This solution is also used to prove a dispersion relation for tae vertex function of the compound particle, and to give an approximate solution. The positiveness of the normalization integral is proved in the nonrelativistic limit. The bound state of nncleon and antinucleon is studied in the ladder-chain approximation, and it is found that the normalization condition gives finite wave function in spite of divergency of the normalization integral. (auth)

- Authors:

- Publication Date:

- Research Org.:
- Maryland. Univ., College Park

- OSTI Identifier:
- 4788754

- Report Number(s):
- AFOSR-2759; TR/262

- NSA Number:
- NSA-16-029470

- DOE Contract Number:
- AF49(638)-24

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: Orig. Receipt Date: 31-DEC-62

- Country of Publication:
- United States

- Language:
- English

- Subject:
- PHYSICS; ANTINUCLEONS; BETHE-SALPETER EQUATION; DISPERSION RELATIONS; ELEMENTARY PARTICLES; FIELD THEORY; INTERACTIONS; MATHEMATICS; NUCLEONS; QUANTUM MECHANICS; RELATIVITY THEORY

### Citation Formats

```
Sato, I.
```*NORMALIZATION CONDITION FOR THE BETHE-SALPETER WAVE FUNCTION AND A FORMAL SOLUTION TO THE BETHE-SALPETER EQUATION*. United States: N. p., 1962.
Web.

```
Sato, I.
```*NORMALIZATION CONDITION FOR THE BETHE-SALPETER WAVE FUNCTION AND A FORMAL SOLUTION TO THE BETHE-SALPETER EQUATION*. United States.

```
Sato, I. Fri .
"NORMALIZATION CONDITION FOR THE BETHE-SALPETER WAVE FUNCTION AND A FORMAL SOLUTION TO THE BETHE-SALPETER EQUATION". United States.
```

```
@article{osti_4788754,
```

title = {NORMALIZATION CONDITION FOR THE BETHE-SALPETER WAVE FUNCTION AND A FORMAL SOLUTION TO THE BETHE-SALPETER EQUATION},

author = {Sato, I},

abstractNote = {By the use of an inhomogeneous Bethe-Salpeter equation a normalization condition for the Bethe-Salpeter wave function is obtained. This condition requires the normalization integral to be positive. A formal solution is obtained in the ladder approximation, and convergence of the normalization integral is proved by the use of this solution. This solution is also used to prove a dispersion relation for tae vertex function of the compound particle, and to give an approximate solution. The positiveness of the normalization integral is proved in the nonrelativistic limit. The bound state of nncleon and antinucleon is studied in the ladder-chain approximation, and it is found that the normalization condition gives finite wave function in spite of divergency of the normalization integral. (auth)},

doi = {},

url = {https://www.osti.gov/biblio/4788754},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1962},

month = {6}

}