One Dimensional Point Interactions and the Resolvent Algebra -- Simple Remarks

Abstract

This paper shows that the resolvent algebra $\mathcal{R}\left( \mathbb{R}^2,\sigma \right)$ can accommodate dynamics induced by self-adjoint Hamiltonians on $L^2\left( \mathbb{R} \right)$ describing a single non-relativistic spinless particle undergoing one up to countably many different fixed point interactions located on the real line.