Spaces of Exact Boundary Controllability of a Schrödinger Equation with an Internal Point Mass

We consider a linear system of PDEs composed of two Schrödinger equations of arbitrary lengths connected by a point mass interface condition. With boundary control active at one end point, we find that the associated spaces of exact controllability may, or may not, possess an asymmetry in regularity on either side of the point mass. The precise way in which the asymmetry occurs is characterized for the case of rational lengths.