CONICET | Buscador de Institutos y Recursos Humanos

In this work we review a recently introduced methodology to solve the Schrödinger equation of three particles. We assume that the particles interact through potentials depending only on the distances between them. Because of the symmetries of the Schrodinger equation, the wave function can be evaluated separately for each L, M, S and P (total angular momentum, its projection along the z axis, the spin symmetry and parity, respectively). We then propose a partial wave expansion in terms of the bi-spherical harmonics, and obtain a coupled set of two-dimensional equations in the radial coordinates r1 and r2. The set of coupled equations is solved by means of a Sturmian expansion (one Sturmian set for each coordinate). The Generalized Sturmian functions are solutions of a Sturm-Liouville equation whith a short range generating potential,β is the eigenvalue and E is considered as a parameter. Constructing the basis in this way enables us to set boundary conditions of the complete problem in each Sturmian depending on coordinates r1 and r2: Kato cusp conditions and Coulomb exponentially decaying behaviour for negative energies, or Coulomb outgoing wave conditions for positiveones. In this work we will show some results of the application of the Sturmian expansion to the solution of the Schrodinger equation for a variety of three-body bounded atomic and molecular systems and models. We choose here using negativeenergy Sturmian functions, and compute ground as well as the different manifolds of excited states. We also analyze differentchoices for the generating potential to achieve a high degree of accuracy in the energies of the states. For an optimal choice of the potential, with 35 Sturmians per electron, we found E=-2.903 712 820 a.u. for the He ground state, (reference value: -2.903 724 377 a.u.).