  We discuss here basic properties of the quantum differential equation of the
Hilbert scheme of points in the plane. Our emphasis is on intertwining
operators (which shift equivariant parameters) and their applications. In
particular, we obtain an exact solution to the connection problem from the
Donaldson-Thomas point q=0 to the Gromov-Witten point q=-1. The paper is an
expanded version of what was once the last Section of arXiv:math/0411210.
