Abstract The objective of this paper is to demonstrate the usefulness of density matrix techniques in the determination of the ground state energy of certain atomic systems. Use of the method, currently under development, results in a lower energy bound in contrast with the Rayleigh-Ritz method which yields an upper bound. The former technique is illustrated for the C⁺⁺ atomic system. It was found that the Pauli Principle was being violated even when the 2-particle density matrix is expanded in...

Abstract The Schrodinger equation for an atomic system which possesses N electrons has 3N independent variables and is perhaps one of the most difficult questions in physics to solve. Because of the complex nature of the problem, only approximate methods can be used. One such method is the Rayleigh-Ritz Variational principle [sic] which minmizes over all [sic] space, and the minimum is the ground state energy. Another method is by...

Abstract The non-relativistic energies have been determined for the singlet and triple S states (1¹S, 2¹S and 2³S) of the helium like two electron system. Calculations were based on a finite set of orbitals of the order 7. The set, which includes Laguerre polynomials, is expressed as a superposition of configurations built up from one-electron wave functions or orbitals and approximates the exact wave function. Application of the variational principle leads to a system of linear equations....