  Borrowing ideas from the relation between classical and quantum mechanics, we
study a non-commutative elevation of the ADE geometries involved in building
Calabi-Yau manifolds. We derive the corresponding geometric hamiltonians and
the holomorphic wave equations representing these non-commutative geometries.
The spectrum of the holomorphic waves is interpreted as the quantum moduli
space. Quantum A_1 geometry is analyzed in some details and is found to be
linked to the Whittaker differential equation.
