Paper Info
Title
Algebraic tools for dealing with the atomic shell model. I. Wavefunctions and integrals for hydrogen-like ions
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 behavior 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.
Year
DOI
Venue
2005
10.1016/j.cpc.2004.09.004
Computer Physics Communications
Keywords
Field
DocType
Analytical solution,Coulomb–Green's function,Coulomb problem,Dirac equation,Energy level,Expectation value,Hydrogen-like ion,Hydrogenic wavefunction,Matrix element,Radial integral,Special functions
Coulomb,Dirac equation,Quantum mechanics,Mathematical analysis,Special functions,Expectation value,Theoretical physics,Wave function,Dirac (video compression format),Hydrogen atom,Quantum optics,Physics
Journal
Volume
Issue
ISSN
165
2
0010-4655
Citations 
PageRank 
References 
2
0.53
1
Authors
3
Name
Order
Citations
PageRank
Andrey Surzhykov130.94
Peter Koval221.20
Stephan Fritzsche352.64