Some Problems of Self-Adjoint Extension in the Schrodinger equation

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 solutions must be retained for definite interval of parameters, which requires performing of Self-Adjoint Extension necessarily. The "Pragmatic approach" is used and some of its consequences are considered for wide class of transitive potentials. The problems of restriction of Self-Adjoint Extension parameter are also discussed. Various relevant applications are presented as well.