# Analytic Coulomb matrix elements in a three-dimensional geometry

## Abstract

Using a complete basis set we have obtained an analytic expression for the matrix elements of the Coulomb interaction. These matrix elements are written in a closed form. We have used the basis set of the three-dimensional isotropic quantum harmonic oscillator in order to develop our calculations, which can be useful when treating interactions in localized systems.

- Authors:

- Department of Physical Sciences, P.O. Box 3000, FIN-90014 University of Oulu (Finland)

- Publication Date:

- OSTI Identifier:
- 20768689

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 46; Journal Issue: 12; Other Information: DOI: 10.1063/1.2146187; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; GEOMETRY; HARMONIC OSCILLATORS; MATRIX ELEMENTS; PARTICLE INTERACTIONS; QUANTUM MECHANICS; THREE-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Garcia, Jaime Zaratiegui.
```*Analytic Coulomb matrix elements in a three-dimensional geometry*. United States: N. p., 2005.
Web. doi:10.1063/1.2146187.

```
Garcia, Jaime Zaratiegui.
```*Analytic Coulomb matrix elements in a three-dimensional geometry*. United States. doi:10.1063/1.2146187.

```
Garcia, Jaime Zaratiegui. Thu .
"Analytic Coulomb matrix elements in a three-dimensional geometry". United States.
doi:10.1063/1.2146187.
```

```
@article{osti_20768689,
```

title = {Analytic Coulomb matrix elements in a three-dimensional geometry},

author = {Garcia, Jaime Zaratiegui},

abstractNote = {Using a complete basis set we have obtained an analytic expression for the matrix elements of the Coulomb interaction. These matrix elements are written in a closed form. We have used the basis set of the three-dimensional isotropic quantum harmonic oscillator in order to develop our calculations, which can be useful when treating interactions in localized systems.},

doi = {10.1063/1.2146187},

journal = {Journal of Mathematical Physics},

number = 12,

volume = 46,

place = {United States},

year = {Thu Dec 15 00:00:00 EST 2005},

month = {Thu Dec 15 00:00:00 EST 2005}

}

DOI: 10.1063/1.2146187

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