dorsal/arxiv
View SchemaAlgebraic tools for dealing with the atomic shell model. I. Wavefunctions and integrals for hydrogen--like ions
| Authors | Andrey Surzhykov, Peter Koval, Stephan Fritzsche |
|---|---|
| Categories | |
| ArXiv ID | physics/0503011 |
| URL | https://arxiv.org/abs/physics/0503011 |
| DOI | 10.1016/j.cpc.2004.09.004 |
| Journal | A. Surzhykov, P. Koval and S. Fritzsche, Comput. Phys. Comm, 165 (2005) 139-156 |
Abstract
Today, the 'hydrogen atom model' is known to play its role not only in teaching the basic elements of quantum mechanics but also for building up effective theories in atomic and molecular physics, quantum optics, plasma physics, or even in the design of semiconductor devices. Therefore, the analytical as well as numerical solutions of the hydrogen--like ions are frequently required both, for analyzing experimental data and for carrying out quite advanced theoretical studies. In order to support a fast and consistent access to these (Coulomb--field) solutions, here we present the Dirac program which has been developed originally for studying the properties and dynamical behaviour of the (hydrogen--like) ions. In the present version, a set of Maple procedures is provided for the Coulomb wave and Green's functions by applying the (wave) equations from both, the nonrelativistic and relativistic theory. Apart from the interactive access to these functions, moreover, a number of radial integrals are also implemented in the Dirac program which may help the user to construct transition amplitudes and cross sections as they occur frequently in the theory of ion--atom and ion--photon collisions.
{
"annotation_id": "6b859d1f-b09e-47c3-bd2a-c8c35ee7d73b",
"date_created": "2026-03-02T18:00:56.921000Z",
"date_modified": "2026-03-02T18:00:56.921000Z",
"file_hash": "9f554a4fc6c3a14608824fdac16fbdbdbbb606cfd6ec92911f4b01a19f53574d",
"private": false,
"record": {
"abstract": "Today, the \u0027hydrogen atom model\u0027 is known to play its role not only in\nteaching the basic elements of quantum mechanics but also for building up\neffective theories in atomic and molecular physics, quantum optics, plasma\nphysics, or even in the design of semiconductor devices. Therefore, the\nanalytical as well as numerical solutions of the hydrogen--like ions are\nfrequently required both, for analyzing experimental data and for carrying out\nquite advanced theoretical studies. In order to support a fast and consistent\naccess to these (Coulomb--field) solutions, here we present the Dirac program\nwhich has been developed originally for studying the properties and dynamical\nbehaviour of the (hydrogen--like) ions. In the present version, a set of Maple\nprocedures is provided for the Coulomb wave and Green\u0027s functions by applying\nthe (wave) equations from both, the nonrelativistic and relativistic theory.\nApart from the interactive access to these functions, moreover, a number of\nradial integrals are also implemented in the Dirac program which may help the\nuser to construct transition amplitudes and cross sections as they occur\nfrequently in the theory of ion--atom and ion--photon collisions.",
"arxiv_id": "physics/0503011",
"authors": [
"Andrey Surzhykov",
"Peter Koval",
"Stephan Fritzsche"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1016/j.cpc.2004.09.004",
"journal_ref": "A. Surzhykov, P. Koval and S. Fritzsche, Comput. Phys. Comm, 165\n (2005) 139-156",
"title": "Algebraic tools for dealing with the atomic shell model. I. Wavefunctions and integrals for hydrogen--like ions",
"url": "https://arxiv.org/abs/physics/0503011"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "3d9a1987-6922-444c-a588-092be7582312",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}