  The Self-Adjoint Extension in the Schrodinger equation for potentials behaved
as an attractive inverse square at the origin is critically reviewed. Original
results are also presented. It is shown that the additional non-regular
solutions must be retained for definite interval of parameters, which requires
a necessity of performing a Self-Adjoint Extension (SAE) procedure of radial
Hamiltonian.The Pragmatic approach is used and some of its consequences are
considered for wide class of transitive potentials. Our consideration is based
on the established earlier by us a boundary condition for the radial wave
function and the corresponding consequences are derived. Various relevant
applications are presented as well. They are: inverse square potential in the
Schrodinger equation is solved when the additional non-regular solution is
retained. Valence electron model and the Klein-Gordon equation with the Coulomb
potential is considered and the hydrino -like levels are discussed.
