Baxter T-Q Equation for Shape Invariant Potentials. The Finite-Gap Potentials Case

Details Baxter T-Q Equation for Shape Invariant Potentials. The Finite-Gap Potentials Case Baxter T-Q Equation for Shape Invariant Potentials. The Finite-Gap Potentials Case

2000-06-10

arxiv.org/abs/hep-th/0006074v2

J.Math.Phys. 43 (2002) 847-865

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, no figures Extended section 10, one reference added. Version accepted for publication in Jurnal of Mathematical Phys

Scientific paper

10.1063/1.1426689

The Darboux transformation applied recurrently on a Schroedinger operator generates what is called a {\em 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.

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