Work

Spectral Parameter Power Series Representation for Regular Solutions of the Radial Dirac System

Year: 2025

Type: article

Abstract: A spectral parameter power series (SPPS) representation for the regular solution of the radial Dirac system with complex coefficients is obtained, as well as a SPPS representation for the (entire) characteristic function of the corresponding spectral problem on a finite interval. Based on the SPPS representation, a numerical method for solving spectral problems is developed. It is shown that the method is also applicable to solving spectral problems for perturbed Bessel equations. We exhibit that the proposed numerical method delivers excellent results. Additionally, an application of the method to find the energy values of an electron orbiting a hydrogen-like atom with a finite radius is presented.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.70231

Authors: Emmanuel Roque, Sergii M. Torba

Institution: Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $5,000

OpenAlex ID: W4415500308

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Cites: 21

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