Until 1975 the Schrödinger equation had rather little to do with modern particle physics, with a few exceptions. After November 1974, when it was understood that the J/ψ was made of heavy quark–antiquark pairs, there was a renewed interest in potential models of hadrons, which continued with the discovery of the b quark in 1977. The parallel with positronium was obvious; this is the origin of the neologism “quarkonium”. However, in contrast to positronium, which is dominated by the Coulomb potential, the potential between quarks was not known and outside explicit numerical calculations with specific models, there was a definite need for new theoretical tools to study the energy levels, partial widths, radiative transitions, etc. for large classes of potentials. This led to the discovery of a large number of completely new rigorous results on the Schrödinger equation which are interesting not only for the qualitative understanding of quarkonium and more generally hadrons but also in themselves and which can be in turn applied to other fields such as atomic physics. All this material is scattered in various physics journals, except for the Physics Reports by Quigg and Rosner on the one hand and by the present authors on the other hand, which are partly obsolete, and the review by one of us (A.M.) in the proceedings of the 1986 Schladming “Internationale Universitätswochen für Kernphysik”, to which we will refer later. There was a clear need to collect the most important exact results and present them in an orderly way.