# Reconstruction of radial Dirac operators

## Abstract

We study the inverse spectral problem of reconstructing the potential of radial Dirac operators acting in the unit ball of R{sup 3}. For each one-dimensional partial Dirac operator corresponding to a nonzero angular momentum, we give a complete description of the spectral data (eigenvalues and suitably defined norming constants), prove existence and uniqueness of solutions to the inverse problem, and present the reconstruction algorithm.

- Authors:

- Institut fuer Angewandte Mathematik, Universitaet Bonn, Wegelerstrasse 6, D-53115, Bonn (Germany)
- (Ukraine) and Lviv University, 1 Universytetska Street, 79602 Lviv (Ukraine)

- Publication Date:

- OSTI Identifier:
- 20929683

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 4; Other Information: DOI: 10.1063/1.2709847; (c) 2007 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; ALGORITHMS; ANGULAR MOMENTUM; DIRAC EQUATION; DIRAC OPERATORS; EIGENVALUES; MATHEMATICAL SOLUTIONS; ONE-DIMENSIONAL CALCULATIONS; POTENTIALS

### Citation Formats

```
Albeverio, S., Hryniv, R., Mykytyuk, Ya., and Institute for Applied Problems of Mechanics and Mathematics, 3B Naukova Street, 79602 Lviv.
```*Reconstruction of radial Dirac operators*. United States: N. p., 2007.
Web. doi:10.1063/1.2709847.

```
Albeverio, S., Hryniv, R., Mykytyuk, Ya., & Institute for Applied Problems of Mechanics and Mathematics, 3B Naukova Street, 79602 Lviv.
```*Reconstruction of radial Dirac operators*. United States. doi:10.1063/1.2709847.

```
Albeverio, S., Hryniv, R., Mykytyuk, Ya., and Institute for Applied Problems of Mechanics and Mathematics, 3B Naukova Street, 79602 Lviv. Sun .
"Reconstruction of radial Dirac operators". United States.
doi:10.1063/1.2709847.
```

```
@article{osti_20929683,
```

title = {Reconstruction of radial Dirac operators},

author = {Albeverio, S. and Hryniv, R. and Mykytyuk, Ya. and Institute for Applied Problems of Mechanics and Mathematics, 3B Naukova Street, 79602 Lviv},

abstractNote = {We study the inverse spectral problem of reconstructing the potential of radial Dirac operators acting in the unit ball of R{sup 3}. For each one-dimensional partial Dirac operator corresponding to a nonzero angular momentum, we give a complete description of the spectral data (eigenvalues and suitably defined norming constants), prove existence and uniqueness of solutions to the inverse problem, and present the reconstruction algorithm.},

doi = {10.1063/1.2709847},

journal = {Journal of Mathematical Physics},

number = 4,

volume = 48,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}

DOI: 10.1063/1.2709847

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