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The Darboux transformation applied recurrently on a Schroedinger operatorgenerates what is called a {\em dressing chain}, or from a different point ofview, a set of supersymmetric shape invariant potentials. The finite-gappotential theory is a special case of the chain. For the finite-gap case, theequations of the chain can be expressed as a time evolution of a Hamiltoniansystem. We apply Sklyanin's method of separation of variables to the chain. Weshow that the classical equation of the separation of variables is the BaxterT-Q relation after quantization.Comment: 25 pages, no figures Extended section 10, one reference added.  Version accepted for publication in Jurnal of Mathematical Physic

Baxter T-Q equation for shape invariant potentials. The finite-gap potentials case