01116nas a2200109   4500008004100000245007800041210006900119520071700188100002900905700002100934856005100955       2016                        en  d00aOn point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians0 apoint interactions realised as TerMartirosyanSkornyakov Hamilton3 aFor quantum systems of zero-range interaction we discuss the mathematical scheme within which modelling the two-body interaction by means of the physically relevant ultra-violet asymptotics known as the ``Ter-Martirosyan--Skornyakov condition'' gives rise to a self-adjoint realisation of the corresponding Hamiltonian. This is done within the self-adjoint extension scheme of Krein, Visik, and Birman. We show that the Ter-Martirosyan--Skornyakov asymptotics is a condition of self-adjointness only when is imposed in suitable functional spaces, and not just as a point-wise asymptotics, and we discuss the consequences of this fact on a model of two identical fermions and a third particle of different nature.1 aMichelangeli, Alessandro1 aOttolini, Andrea  uhttp://urania.sissa.it/xmlui/handle/1963/35195