The Generalized Sturmian Method

The generalized Sturmian Library (Sturmian) is a C library and a collection of programs (primarily written in Mathematica) for calculating the electronic structure, spectra and properties of atoms and atomic ions using the generalized Sturmian method.

The generalized Sturmian method is a novel and promising approach to the many particle problem in quantum theory, i.e. to the problem of calculating microphysical properties of matter from first principles.

The method makes use of basis sets that are isoenergetic solutions to an approximate many-particle Schroedinger equation with a weighted potential V₀. The weighting factors are chosen in such a way as to make all the members of the basis set correspond to the energy of the state being represented.

It is not unusual in quantum theory to build up solutions to a many-particle Schroedinger equation from basis functions that are solutions to an approximate many-particle equation. What is unusual in the generalized Sturmian method is that all the members of the basis set correspond to the energy of the state being represented. It is because of this property, that generalized Sturmian basis sets lead to rapidly convergent solutions.

The focus of our work has been the case where V₀ is chosen to be the attraction of the bare nucleus. In this case, the approximate Schroedinger equation can be solved exactly. The solutions are Slater determinants of hydrogenlike atomic spin-orbitals with a weighted charge Q that is the same throughout the determinant, but different for each configuration. These serve as scaling parameters that make the turning point behaviour of each basis function appropriate for the synthesis of the desired wave function. The scaling parameters are in this case obtained automatically when the generalized Sturmian secular equation is solved.