# Four Euclidean conformal group in atomic calculations: Exact analytical expressions for the bound-bound two-photon transition matrix elements in the H atom

## Abstract

By combining Sturmian-Coulomb techniques with a local representation of the four Euclidean conformal group SU* (4) approx. =Spin(1,5), a compact analytical form, suitable for any analytic continuation on the energy variable, is obtained for the following bound-bound two-photon transition matrix element in the H atom: I/sub NNprime/(E) =,where G(E) is the Coulomb Green's function.

- Authors:

- Publication Date:

- Research Org.:
- Laboratoire de Chimie Physique de l'Universite Pierre et Marie Curie, 75231 Paris Cedex 05, France

- OSTI Identifier:
- 5076647

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: J. Math. Phys. (N.Y.); (United States); Journal Volume: 19:5

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; HYDROGEN; ENERGY-LEVEL TRANSITIONS; CONFORMAL GROUPS; EUCLIDEAN SPACE; GREEN FUNCTION; MATRIX ELEMENTS; SCHROEDINGER EQUATION; SU GROUPS; CRYOGENIC FLUIDS; DIFFERENTIAL EQUATIONS; ELEMENTS; EQUATIONS; FLUIDS; FUNCTIONS; LIE GROUPS; MATHEMATICAL SPACE; NONMETALS; RIEMANN SPACE; SPACE; SYMMETRY GROUPS; WAVE EQUATIONS; 640302* - Atomic, Molecular & Chemical Physics- Atomic & Molecular Properties & Theory

### Citation Formats

```
Gazeau, J.P.
```*Four Euclidean conformal group in atomic calculations: Exact analytical expressions for the bound-bound two-photon transition matrix elements in the H atom*. United States: N. p., 1978.
Web. doi:10.1063/1.523766.

```
Gazeau, J.P.
```*Four Euclidean conformal group in atomic calculations: Exact analytical expressions for the bound-bound two-photon transition matrix elements in the H atom*. United States. doi:10.1063/1.523766.

```
Gazeau, J.P. Mon .
"Four Euclidean conformal group in atomic calculations: Exact analytical expressions for the bound-bound two-photon transition matrix elements in the H atom". United States. doi:10.1063/1.523766.
```

```
@article{osti_5076647,
```

title = {Four Euclidean conformal group in atomic calculations: Exact analytical expressions for the bound-bound two-photon transition matrix elements in the H atom},

author = {Gazeau, J.P.},

abstractNote = {By combining Sturmian-Coulomb techniques with a local representation of the four Euclidean conformal group SU* (4) approx. =Spin(1,5), a compact analytical form, suitable for any analytic continuation on the energy variable, is obtained for the following bound-bound two-photon transition matrix element in the H atom: I/sub NNprime/(E) =,where G(E) is the Coulomb Green's function.},

doi = {10.1063/1.523766},

journal = {J. Math. Phys. (N.Y.); (United States)},

number = ,

volume = 19:5,

place = {United States},

year = {Mon May 01 00:00:00 EDT 1978},

month = {Mon May 01 00:00:00 EDT 1978}

}

DOI: 10.1063/1.523766

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