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

The Darboux transformation applied recurrently on a Schrodinger operator generates what is called a dressing chain, or from a different point of view, a set of supersymmetric shape invariant potentials. The finite-gap potential theory is a special case of the chain. For the finite-gap case, the equations of the chain can be expressed as a time evolution of a Hamiltonian system. We apply Sklyanin's method of separation of variables to the chain. We show that the classical equation of the separation of variables is the Baxter T-Q relation after quantization. (C) 2002 American Institute of Physics.