The linear Schrodinger equation is central to Quantum Chemistry. It is presented within the context of relativistic Quantum Mechanics and analysed both in time-dependent and time-independent forms. The Riccati equation is used to study the one-dimensional Schrodinger equation.
The authors develop the Schrodinger-Riccati equation as an approach to determine solutions of the time-independent, linear Schrodinger equation."

Impressive advances have been made in the study of atomic structures, at both the experimental and theoretical levels. And yet, the scarcity of information on atomic energy levels is evident At the same time there exists a need for data, because of the developments in such diverse fields as astrophysics and plasma and laser research, all of them of fundamental importance as well as practical impact. This project of research in atomic structure, consisting of three components (formulation, computer program, and numerical results), constitutes a basic and comprehensive work with a variety of uses. In its most practical application, it will yield a rather accurate prediction of the energy levels of any atomic system, of use per se or in the interpretation and confirmation of experimental results. On the other hand, it will also be of use in the comparative study of the appropriateness of the various levels of approximation and as a point of reference.