Abstract An improved ground state wavefunction for Helium for use in density matrix calculations has been obtained. This improvement was achieved by the introduction into the expansion for the singlet S-state wavefunction for Helium, of a term containing explicit angular dependence. This angular term was constructed so as to preserve angular momentum symmetry by being an eigenfunction of the two-particle, angular momentum operator with eigenvalue zero, as is required for S-states. The results give...

Abstract

A recently developed theory enabling the construction of density matrices which are expressible in terms of a given spin geminal set and which are a nearly N-representable as possible is discussed.

Calculation of lower bounds to the ground state energy of the C⁺⁺ ion is performed utilizing reduced density matrices subject to the continuously variable N-representability constraint determined by the above mentioned theory.

Abstract In Part I, a large parameter asymptotic expansion of a perturbed simple harmonic oscillator is presented. Perturbations of the form λx∝ are studied were λ is the coupling constant. The method is demonstrated by a general derviation of the wavefunctions to third order for any ∝ and quantum number n. Additonal expressions are presented for the ground states to tenth order in the energy. It is also shown that the "matching condition" for the basic and...

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....