Continuous and Discrete Algorithms in Quantum Chemistry: Polynomial Sets, Spin Networks and Sturmian Orbitals

An effort is accounted for in the present paper to exhibit the recently actively investigated connection between the search and use of ”orbitals” as basis sets in applied quantum mechanics and current advances in the mathematics of special functions and orthogonal polynomials, which are in turn motivated by the developments of the quantum theory of angular momentum. The latter theory in modern applications forms the basis for the class of ”spin-network” algorithms. These ”orbitals” enjoy important properties regarding orthogonality and completeness. In configuration space, they are often designated as Kepler-Coulomb Sturmian orbitals, in momentum space they are intimately connected with hyperspherical harmonics. The paper contains a brief presentation including also computational results and a discussion oriented towards the numerical use of these orbitals.