  Spectral transformation is known to set up a birational morphism between the
Hitchin and Beauville-Mukai integrable systems. The corresponding phase spaces
are: (a) the cotangent bundle of the moduli space of bundles over a curve C,
and (b) a symmetric power of the cotangent surface T^*(C). We conjecture that
this morphism can be quantized, and we check this conjecture in the case where
C is a rational curve with marked points and rank 2 bundles. We discuss the
relation of the resulting isomorphism of quantized algebras with Sklyanin's
separation of variables.
