  We give a differential geometric construction of a connection in the bundle
of quantum Hilbert spaces arising from half-form corrected geometric
quantization of a prequantizable, symplectic manifold, endowed with a rigid,
family of K\"ahler structures, all of which give vanishing first Dolbeault
cohomology groups. In [And1] Andersen gave an explicit construction of
Hitchin's connection in the non-corrected case using additional assumptions.
Under the same assumptions we also give an explicit solution in terms of Ricci
potentials. Morover we show that if these are carefully chosen the construction
coincides with the construction of Andersen in the non-corrected case.
