Resolving the spurious-state problem in Dirac equation by using the staggered-grid method
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911226259308544 |
|---|---|
| author | Li, Lingfeng Shen, Hong Hu, Jinniu Zhang, Ying |
| author_facet | Li, Lingfeng Shen, Hong Hu, Jinniu Zhang, Ying |
| contents | Discretizing the Dirac equation on a uniform grid with the central difference formula often generates spurious states. We propose a staggered-grid scheme in the framework of the finite-difference method that suppresses these spurious states without introducing Wilson terms or ad-hoc filtering. In this approach, the large and small components of the Dirac equation are placed on interlaced nodes, and the first-order derivatives are evaluated between staggered points, yielding a Hamiltonian that breaks the unitary transformation between $H_κ$ and $H_{-κ}$. Benchmarks with the nuclear Woods-Saxon potentials demonstrate one-to-one agreement with the eigenvalues obtained from shooting method and asymmetric finite-difference method, rapid convergence for weakly bound states, and reduced box-size sensitivity. The method retains the simplicity of central differences and standard matrix diagonalization, while naturally extending to higher-order and multi-dimension systems. It provides a compact and efficient tool for relativistic bound-state and scattering calculations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19201 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Resolving the spurious-state problem in Dirac equation by using the staggered-grid method Li, Lingfeng Shen, Hong Hu, Jinniu Zhang, Ying Nuclear Theory Discretizing the Dirac equation on a uniform grid with the central difference formula often generates spurious states. We propose a staggered-grid scheme in the framework of the finite-difference method that suppresses these spurious states without introducing Wilson terms or ad-hoc filtering. In this approach, the large and small components of the Dirac equation are placed on interlaced nodes, and the first-order derivatives are evaluated between staggered points, yielding a Hamiltonian that breaks the unitary transformation between $H_κ$ and $H_{-κ}$. Benchmarks with the nuclear Woods-Saxon potentials demonstrate one-to-one agreement with the eigenvalues obtained from shooting method and asymmetric finite-difference method, rapid convergence for weakly bound states, and reduced box-size sensitivity. The method retains the simplicity of central differences and standard matrix diagonalization, while naturally extending to higher-order and multi-dimension systems. It provides a compact and efficient tool for relativistic bound-state and scattering calculations. |
| title | Resolving the spurious-state problem in Dirac equation by using the staggered-grid method |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2510.19201 |