Quantum Gel′fand-Levitan Equations for Jost Functions Associated with Bound States of the Nonlinear Schrodinger Model

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  • Nakawaki Yuji
    Division of Physics and Mathematics, Faculty of Engineering, Setsunan University

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  • Quantum Gel’fand-Levitan Equations for Jost Functions Associated with Bound States of the Nonlinear Schrödinger Model
  • Quantum Gel fand Levitan Equations for

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To complete solving the nonlinear Schrödinger model by means of the quantum inverse scattering method, we realize scattering data operators including those for bound states in terms of reflection coefficient operators in the framework of the inverse problem. To this end, we formulate quantum Gel’fand-Levitan equations for Jost solutions of generalized Zakharov-Shabat eigenvalue problems. Our formulation becomes simpler and clearer than that of Göckeler because we fully use the newly found fact that in the similar manner as the classical case one of Jost solutions can be described in terms of linearly independent ones for each n (n=1, 2, 3, …). We also verify operator identities among Jost solutions for each n which are indispensable to express discontinuities of piecewise analytic operators in such a way that we obtain closed Gel’fand-Levitan equations.

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