Partitioning technique procedure revisited: Formalism and first application to atomic problems

Abstract

Usually the partitioning technique (PT) has been studied under two aspects: (i) as a numerical tool for solving secular equations of high order, and (ii) as a theoretical method related to the infinite‐order perturbation theory and the iteration–variation methods. Here it is shown that there exists a form of the PT equations which allows us to determine explicitly the spectrum and eigenstates of the Hamiltonian operator for different forms of potentials without the utilization of perturbative expansions or iterative equations of the type E=f(E). As a first application of the new approach, we consider the hydrogen‐atom in strong magnetic fields (B ~ 109 G).