TY - RPRT
T1 - On point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians
Y1 - 2016
A1 - Alessandro Michelangeli
A1 - Andrea Ottolini
AB - 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.
UR - http://urania.sissa.it/xmlui/handle/1963/35195
U1 - 35489
U2 - Mathematics
U4 - 1
U5 - MAT/07
ER -