Abstract
For nonadditive finite-dimensional perturbations of a Hermitian operator, with the aid of M. G. Krein's formula for generalized resolvents, one derives a representation of all scattering suboperators, parametrized by Hermitian matrices. On the basis of this representation, one obtains explicit expressions for a series of new, exactly solvable quantum models with null-range potential. One establishes a connection between the obtained parametrizations with phenomenological S matrices and the corresponding Wigner R functions.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 149, pp. 7–23, 1986.
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Adamyan, V.M., Pavlov, B.S. Null-range potentials and M. G. Krein's formula for generalized resolvents. J Math Sci 42, 1537–1550 (1988). https://doi.org/10.1007/BF01665040
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DOI: https://doi.org/10.1007/BF01665040