On point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians
Abstract
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 pointwise asymptotics, and we discuss the consequences of this fact on a model of two identical fermions and a third particle of different nature.
Keywords
Cite
@article{arxiv.1606.05222,
title = {On point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians},
author = {Alessandro Michelangeli and Andrea Ottolini},
journal= {arXiv preprint arXiv:1606.05222},
year = {2017}
}
Comments
Published on: Report on Mathematical Physics 2016