# On the Use of Lambert W Function for Modeling of Quantum Resonances

## Abstract

The Lambert W function is used to represent data (bound state energies) for the process of analytical continuation in the coupling constant. It is shown how the presence of the singularity of the W function restricts the accuracy of determination of the branch point. The accuracy of the determination of resonance parameters is also discussed. It is shown that even for moderately accurate input data the process of analytical continuation yields resonance parameters of accuracy surpassing modern experimental data.

- Authors:

- Faculty of Mathematics and Physics, Charles University in Prague, V Holesovickach 2, 180 00 Praha 8 (Czech Republic)

- Publication Date:

- OSTI Identifier:
- 21611602

- Resource Type:
- Journal Article

- Journal Name:
- AIP Conference Proceedings

- Additional Journal Information:
- Journal Volume: 1389; Journal Issue: 1; Conference: ICNAAM 2011: Conference on numerical analysis and applied mathematics, Halkidiki (Greece), 19-25 Sep 2011; Other Information: DOI: 10.1063/1.3636934; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; BOUND STATE; COUPLING CONSTANTS; FUNCTIONS; GEOMETRY; QUANTUM COMPUTERS; QUANTUM MECHANICS; RESONANCE; SINGULARITY; COMPUTERS; MATHEMATICS; MECHANICS

### Citation Formats

```
Horacek, Jiri, and Ledvinka, Tomas.
```*On the Use of Lambert W Function for Modeling of Quantum Resonances*. United States: N. p., 2011.
Web. doi:10.1063/1.3636934.

```
Horacek, Jiri, & Ledvinka, Tomas.
```*On the Use of Lambert W Function for Modeling of Quantum Resonances*. United States. doi:10.1063/1.3636934.

```
Horacek, Jiri, and Ledvinka, Tomas. Wed .
"On the Use of Lambert W Function for Modeling of Quantum Resonances". United States. doi:10.1063/1.3636934.
```

```
@article{osti_21611602,
```

title = {On the Use of Lambert W Function for Modeling of Quantum Resonances},

author = {Horacek, Jiri and Ledvinka, Tomas},

abstractNote = {The Lambert W function is used to represent data (bound state energies) for the process of analytical continuation in the coupling constant. It is shown how the presence of the singularity of the W function restricts the accuracy of determination of the branch point. The accuracy of the determination of resonance parameters is also discussed. It is shown that even for moderately accurate input data the process of analytical continuation yields resonance parameters of accuracy surpassing modern experimental data.},

doi = {10.1063/1.3636934},

journal = {AIP Conference Proceedings},

issn = {0094-243X},

number = 1,

volume = 1389,

place = {United States},

year = {2011},

month = {9}

}

DOI: 10.1063/1.3636934

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