A technique for generating approximate solutions and it´s application to Coulomb interactions

This paper presents a technique for applying evolutionary computation techniques, particularly genetic algorithms, to the generation of approximate solutions of equations and sets of equations. The technique is applied to the solution of an eigenvalue differential equation of physical significance, the Schrodinger equation, which is addressed for two- and three- center Coulomb potentials. The technique is found to be effective for the two-center case. Consideration of the three-center case reveals a constraint which is different from the constraints used by other techniques to address the same problem. The issue of parasitic solutions is addressed, and a reformulation of the technique is found to avoid this issue and produce reasonable results.