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The Self-Adjoint Extension in the Schrodinger equation for potentials behavedas an attractive inverse square at the origin is critically reviewed. Originalresults are also presented. It is shown that the additional solutions must beretained for definite interval of parameters, which requires performing ofSelf-Adjoint Extension necessarily. The "Pragmatic approach" is used and someof its consequences are considered for wide class of transitive potentials. Theproblems of restriction of Self-Adjoint Extension parameter are also discussed.Various relevant applications are presented as well.

Some Problems of Self-Adjoint Extension in the Schrodinger equation