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Multidimensional and Three-Body Inverse Scattering Problems in the Adiabatic Representation

  • Conference paper
Quantum Inversion Theory and Applications

Part of the book series: Lecture Notes in Physics ((LNP,volume 427))

Abstract

In the adiabatic representation, the multidimensional and three-body inverse scattering problems are discussed on the basis of consistent formulation of both the multichannel inverse problem for gauge systems of equations describing “slow” dynamics of the system, and the parametric one for “fast” dynamics. The method of constructing a wide class of exactly solvable multidimensional models is investigated by comparing the Bargmann potentials with the parametric family of inverse problems and systems of equations with covariant derivatives. A problem introducing an extra matrix of scalar potentials so as to conserve supersymmetry and thus conditions for topological effects is studied. A direct generalization of the Witten supersymmetric quantum mechanics for gauge equations with additional scalar potentials is given. Coupling of supersymmetry and geometric phases and the influence of additional scalar potentials under the degeneracy of the ground state, and as a result under topological effects, are discussed. Algebraic Bargmann and Darboux transformations for equations of a more general form than the Schroedinger ones with an additional functional dependence (h(r)) in the right-hand side of equations are constructed.

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Author information

Authors and Affiliations

  1. Laboratory of Theoretical Physics, Joint Institute for Nuclear Research (Dubna), Head Post Office, P.O.Box 79, Moscow, 101 000, Russia

    A. A. Suzko

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  1. A. A. Suzko
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Editor information

Editors and Affiliations

  1. Theoretische Kernphysik, Universität Hamburg, Luruper Chaussee 149, D-22761, Hamburg, Germany

    H. V. von Geramb

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Suzko, A.A. (1994). Multidimensional and Three-Body Inverse Scattering Problems in the Adiabatic Representation. In: von Geramb, H.V. (eds) Quantum Inversion Theory and Applications. Lecture Notes in Physics, vol 427. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13969-1_6

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