%0 Report %D 2016 %T On point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians %A Alessandro Michelangeli %A Andrea Ottolini %X For 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. %G en %U http://urania.sissa.it/xmlui/handle/1963/35195 %1 35489 %2 Mathematics %4 1 %# MAT/07 %$ Submitted by aottolini@sissa.it (aottolini@sissa.it) on 2016-06-16T11:35:16Z No. of bitstreams: 1 SISSA_preprint_11-2016-MATE.pdf: 288426 bytes, checksum: 1cd4fd0554e316274d2160eaecb2646e (MD5)