Quantum Gel'fand-Levitan Equations for Jost Functions Associated with Bound States of the Nonlinear Schrodinger Model
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概要
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To complete solving the nonlinear Schr6dinger model by means of the quantum in-verse scattering method, we realize scattering data operators including those forbound states in terms of reflection coefficient operators in the framework of the inverse problem. To this end, we formulate quantum Gel'fand-Levitan equations forJost solutions of generalized Zakharov-Shabat eigenvalue problems. Our formulalion becomes simpler and clearer than that of G6ckeler because we fully use the newlyfound fact that in the similar manner as the classical case one of Jost solutions can bedescribed in terms of Iinearly independent ones for each n (z=1, 2, 3,? { ?). We alsoverify operator identities among Jost solutions for each n which are indispensable toexpress discontinuities of piecewise analytic operators in such a way that we obtainclosed Gel'fand-Levitan eq uations.
- 社団法人日本物理学会の論文
- 1990-09-15
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