On Potentials Integrated by the Nikiforov-Uvarov Method

Abstract

We discuss basic potentials of the nonrelativistic and relativistic quantum mechanics that can be integrated in the Nikiforov and Uvarov paradigm with the aid of a computer algebra system. This approach may help the readers to study modern analytical methods of quantum physics.Building on ideas of de Broglie and Einstein, I tried to show that the ordinary differential equations of mechanics, which attempt to define the co-ordinates of a mechanical system as functions of the time, are no longer applicable for "small" systems; instead there must be introduced a certain partial differential equation, which defines a variable ψ ("wave function") as a function of the co-ordinates and the time.