The Pseudospectral Method for the Dirac Equation with Confining Potential
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916044543623168 |
|---|---|
| author | Liu, Dengshan Xie, Huihui Du, Pengxiang Li, Jian Naito, Tomoya |
| author_facet | Liu, Dengshan Xie, Huihui Du, Pengxiang Li, Jian Naito, Tomoya |
| contents | We observe that solving the Dirac equation for confined potentials using the generalized pseudospectral (GPS) method leads to deteriorating convergence of energy eigenvalues and highly oscillatory in wave functions as the confinement radius decreases. It is found that this issue stems from the first-order differentiation formulation employed in GPS method. Motivated by this insight, we adopt the kinetically balanced generalized pseudospectral method, which incorporates the kinetically-balanced condition into the GPS method. Numerical results demonstrate that the mono-kinetically-balanced generalized pseu dospectral (MKB-GPS) method yields converged energy eigenvalues and generates smooth, continuous wave functions. This is the first application of the MKB-GPS method to confined potentials, and its effectiveness is validated for small confinement radii. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25390 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Pseudospectral Method for the Dirac Equation with Confining Potential Liu, Dengshan Xie, Huihui Du, Pengxiang Li, Jian Naito, Tomoya Atomic Physics Mathematical Physics Nuclear Theory Computational Physics We observe that solving the Dirac equation for confined potentials using the generalized pseudospectral (GPS) method leads to deteriorating convergence of energy eigenvalues and highly oscillatory in wave functions as the confinement radius decreases. It is found that this issue stems from the first-order differentiation formulation employed in GPS method. Motivated by this insight, we adopt the kinetically balanced generalized pseudospectral method, which incorporates the kinetically-balanced condition into the GPS method. Numerical results demonstrate that the mono-kinetically-balanced generalized pseu dospectral (MKB-GPS) method yields converged energy eigenvalues and generates smooth, continuous wave functions. This is the first application of the MKB-GPS method to confined potentials, and its effectiveness is validated for small confinement radii. |
| title | The Pseudospectral Method for the Dirac Equation with Confining Potential |
| topic | Atomic Physics Mathematical Physics Nuclear Theory Computational Physics |
| url | https://arxiv.org/abs/2605.25390 |