  We construct the Baxter's operator and the corresponding Baxter's equation
for a quantum version of the Ablowitz Ladik model. The result is achieved by
looking at the quantum analogue of the classical Backlund transformations. For
comparison we find the same result by using the well-known Bethe ansatz
technique. General results about integrable models governed by the same
r-matrix algebra will be given. The Baxter's equation comes out to be a
q-difference equation involving both the trace and the quantum determinant of
the monodromy matrix. The spectrality property of the classical Backlund
transformations gives a trace formula representing the classical analogue of
the Baxter's equation. An explicit q-integral representation of the Baxter's
operator is discussed.
