  In an earlier paper we conjectured a relation between the quantum $\mathcal
D$-modules of a smooth variety $X$ and the projectivisation of a direct sum of
line bundles over it. In this paper we prove the conjecture when $X$ is a
complete intersection in a toric variety. We also use the conjecture to show
that the relations of the small quantum cohomology ring of $X$ that come from
differential operators lift to the projective bundle. The basic cohomology
relation of the projective bundle deforms to a relation in the small quantum
cohomology.
