Many-particle Sturmians

Abstract

The weighted orthonormality relations for many-particle Sturmian basis functions are derived both in momentum space and in position space. It is shown that when these functions are used as a basis, the kinetic energy term disappears from the Schrodinger equation. A general method is developed for constructing many-electron Sturmian basis sets from one-electron Sturmians. This method is illustrated by applications to atoms and ions and to the H2 molecule. It is shown that the direct solution of the Schrodinger equation using many-particle Sturmianbasis functions offers a useful alternative to the Hartree–Fock approximation and configuration interaction; and it is shown that the Sturmian method leads to an automatic optimization of the orbital exponents.