HYPERSPHERICAL STURMIAN BASIS FUNCTIONS

A Sturmian basis set is a set of solutions to the Schrodinger equation, with the potential scaled in such a way that all the members of the set correspond to the same value of the energy. We discuss, in particular, the set of Sturmian basis functions corresponding to solutions of the d-dimensional hydrogenlike wave equation. These hydrogenlike Sturmian functions are expressed in terms of Laguerre polynomials and hyperspherical harmonics. When they are used as a basis for solving the many-particle Schrodinger equation, the secular equations take on a simple form [Eq. (59)]. The necessary integrals are evaluated explicitly, and the possibility of combining the hyperspherical technique with dimensional scaling is discussed.