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    Group-theoretical approach to a non-central extension of the Kepler-Coulomb problem
    (Iop Publishing Ltd, 2010) Kerimov, G. A.; Ventura, A.
    Bound and scattering states of a non-central extension of the three-dimensional Kepler-Coulomb Hamiltonian are worked out analytically within the framework of the potential groups of the problem, SO(7) for bound states and SO(6, 1) for scattering states. In the latter case, the S-matrix is calculated by the method of intertwining operators.
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    Group-theoretical approach to reflectionless potentials
    (Amer Inst Physics, 2006) Kerimov, G. A.; Ventura, A.
    We examine the general form of potentials with zero reflection coefficient in one-dimensional Hamiltonians connected with Casimir invariants of non-compact groups. (c) 2006 American Institute of Physics.
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    Lie-algebraic interpretation of the maximal superintegrability and exact solvability of the Coulomb-Rosochatius potential in n dimensions
    (Iop Publishing Ltd, 2011) Kerimov, G. A.; Ventura, A.
    The potential group method is applied to the n-dimensional Coulomb-Rosochatius potential, whose bound states and scattering states are worked out in detail. As far as scattering is concerned, the S-matrix elements are computed by the method of intertwining operators and an integral representation is obtained for the scattering amplitude. It is shown that the maximal superintegrability of the system is due to the underlying potential group and that the 2n - 1 integrals of motion are related to Casimir operators of subgroups.
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    On algebraic models of relativistic scattering
    (Iop Publishing Ltd, 2008) Kerimov, G. A.; Ventura, A.
    In this paper we develop an algebraic technique for building relativistic models in the framework of the direct-interaction theories. The interacting mass operator M in the Bakamjian-Thomas construction is related to a quadratic Casimir operator C of a non-compact group G. As a consequence, the S matrix can be gained from an intertwining relation between Weyl-equivalent representations of G. The method is illustrated by explicit application to a model with SO(3, 1) dynamical symmetry.