2000/06/30 by Ovidiu Lipan, Constantin Rasinariu · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Canonical transformation #Hamiltonian (control theory) #Hamiltonian formalism #Hamiltonian system #Invariant (physics) #Nonlinear Waves and Solitons #Operator (biology) #Quantum Mechanics and Non-Hermitian Physics #Separation of variables #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1063/1.1426689
published in Journal of Mathematical Physics 43(2), 847-865 (American Institute of Physics) · 25 pages, no figures Extended section 10, one reference added. Version accepted for publication in Jurnal of Mathematical Physics
arxiv created 2001/10/16 · openalex publication_date 2002/02/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The Darboux transformation applied recurrently on a Schrödinger 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.