Two-dimensional Sturmian basis set for bound state calculations

Abstract

Abstract Sturmian functions (SF) constitute a very useful spectral tool to deal with bound states or break-up problems in atomic and molecular physics. In their standard form for the three-body case, the radial part of the wave function is proposed as an expansion in products of one-dimensional generalized SF (GSF). Here, we present an alternative spectral approach. It is based on solutions of a two-dimensional Sturmian eigenvalue problem that is solved with a finite set of one-dimensional GSF. The resulting 2DSF basis set functions depend simultaneously on two interparticle distances and possess a natural reordering. Through calculations of the Helium ground and 41F excited states energy, we compare the efficiency of the two equivalent sets of functions. The superiority of the two-dimensional approach demonstrated here should be particularly useful to reduce computational costs for applications in the continuum regime.