IMPROVED METHOD FOR QUANTUM-MECHANICAL 3-BODY PROBLEM .3. USE OF STURMIAN FUNCTIONS

We extend previous work on the ground state of the symmetric three-body problem by expanding the two-body orbitals φ(k, K) or φ(k, א) (one and three dimensions, respectively) in a set of Sturmian functions. This retains the advantages of the previous expansions, and gains several new ones as well. Among these are a simplification of the equations and a transparent way of estimating convergence. The one-dimensional problem is reduced to an infinite set of coupled integral equations in one variable and the three-dimensional one to a doubly infinite set. As an application and a test of convergence we have solved the one-dimensional equations numerically in successive truncations. We find that keeping only the first term of the set yields results typically accurate to a fraction of a percent.