Representation of solutions of the one-dimensional Dirac equation in terms of Neumann series of Bessel functions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908852638711808 |
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| author | Roque, Emmanuel Torba, Sergii M. |
| author_facet | Roque, Emmanuel Torba, Sergii M. |
| contents | A representation of solutions of the one-dimensional Dirac equation is obtained. The solutions are represented as Neumann series of Bessel functions. The representations are shown to be uniformly convergent with respect to the spectral parameter. Explicit formulas for the coefficients are obtained via a system of recursive integrals. The result is based on the Fourier-Legendre series expansion of the transmutation kernel. An efficient numerical method for solving initial-value and spectral problems based on this approach is presented with a numerical example. The method can compute large sets of eigendata with non-deteriorating accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00303 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representation of solutions of the one-dimensional Dirac equation in terms of Neumann series of Bessel functions Roque, Emmanuel Torba, Sergii M. Classical Analysis and ODEs Numerical Analysis Mathematical Physics 34A25, 34A30, 34A45, 34B30, 34L40, 35L40, 33C45, 65L05, 65L15, 81Q05 A representation of solutions of the one-dimensional Dirac equation is obtained. The solutions are represented as Neumann series of Bessel functions. The representations are shown to be uniformly convergent with respect to the spectral parameter. Explicit formulas for the coefficients are obtained via a system of recursive integrals. The result is based on the Fourier-Legendre series expansion of the transmutation kernel. An efficient numerical method for solving initial-value and spectral problems based on this approach is presented with a numerical example. The method can compute large sets of eigendata with non-deteriorating accuracy. |
| title | Representation of solutions of the one-dimensional Dirac equation in terms of Neumann series of Bessel functions |
| topic | Classical Analysis and ODEs Numerical Analysis Mathematical Physics 34A25, 34A30, 34A45, 34B30, 34L40, 35L40, 33C45, 65L05, 65L15, 81Q05 |
| url | https://arxiv.org/abs/2502.00303 |