Two-body Coulomb problems with sources

Abstract

The two-body Coulomb Schrödinger equation with different types of nonhomogeneities are studied. The particular solution of these nonhomogeneous equations is expressed in closed form in terms of a two-variable hypergeometric function. A particular representation of the latter allows one to study efficiently the solution in the asymptotic limit of large values of the coordinate and hence the associated physics. Simple sources are first considered, and a complete analysis of scattering and bound states is performed. The solutions corresponding to more general (arbitrary) sources are then provided and written in terms of more general hypergeometric functions.

Two-body Coulomb scattering and complex scaling

“…We mention that the driven Schrödinger equation (19) has been studied in [20]. For quite general sources, very complicated analytic solutions can be found [20].…”

“…For quite general sources, very complicated analytic solutions can be found [20]. The aim of our paper is to derive an easy numerical method to solve (19) and, from the scattered part of the wave function, deduce the scattering amplitude.…”

“…We mention that the two-body Coulomb problem with a source term has been recently thoroughly investigated in [20]. Complicated but exact solutions have been given for very general sources.…”

Enzymatic synthesis of L‐lactic acid from carbon dioxide and ethanol with an inherent cofactor regeneration cycle

“…). A third category, deals with wave functions (typically Hylleraas‐type) and energies of quality which are intermediate between the two already mentioned (see, e.g.,24–31). All these trial wave functions have separate, and possibly complementary, purposes: obtain very accurate mean quantities (including the energy), search for a solution as formal as possible, or useful for applications such as collision studies.…”

“…Motivated by collisional studies involving two‐electron atoms, Gasaneo and Ancarani30, 31 introduced a C3‐like basis set which fully diagonalizes the whole diagonal part of the kinetic energy and all the Coulomb interactions (see Section 2 below). The use of such a correlated basis in a Configuration Interaction approach is based on a decomposition of the three‐body wave function in a sum of doubly correlated configurations31; each configuration depends explicitly on the three interelectronic coordinates. The efficiency of the method, called Angular Correlated Configuration Interaction (ACCI), has been illustrated with applications to the helium isoelectronic sequence in the infinite mass approximation31.…”