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 suppor... Title of program: DIRAC Catalogue Id: ADUQ_v1_0 Nature of problem Analytical solutions of the hydrogen atom are widely used in very different fields of physics [2,3]. Despite the rather simple structure of the hydrogen-like ions, however, the underlying 'mathematics' is not always that easy to deal with. Apart from the well-known level structure of these ions as obtained from either the Schrodinger or Dirac equation, namely, a great deal of other properties are often needed. These properties are related to the interaction of bound electron(s) with external par ... Versions of this program held in the CPC repository in Mendeley Data ADUQ_v1_0; DIRAC; 10.1016/j.cpc.2004.09.004 ADUQ_v2_0; DIRAC; 10.1016/j.cpc.2009.11.010 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)