Journal
COMPUTER PHYSICS COMMUNICATIONS
Volume 165, Issue 2, Pages 139-156Publisher
ELSEVIER
DOI: 10.1016/j.cpc.2004.09.004
Keywords
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
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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.
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