  We prove that the periodic quantum Toda lattice corresponding to any extended
Dynkin diagram is completely integrable. This has been conjectured and proved
in all classical cases and $E_6$ by Goodman and Wallach at the beginning of the
1980's. As a direct application, in the context of quantum cohomology of affine
flag manifolds, results that were known to hold only for some particular Lie
types can now be extended to all types.
