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 TMF, 1974, Volume 20, Number 2, Pages 211–222 (Mi tmf3816)

Properties of unitary and nonunitary $S$-matrix on the basis of causality and the completeness condition of wave functions

V. S. Ol'khovskii

Abstract: A study is made of the general properties of the one-charmei unitary and non-unitary $S$-matrix in the case when the interaction inside a sphere of finite radius is unknown while outside the sphere there is a centrifugal barrier plus a noaasingular potential “tail” that decreases asymptotically not weaker than exponentially. Use is made of the completeness condition of a solution of the Schrödinger equation outside the sphere of unknown interaction, symmetry, and generalized unitarity of the $S$-matrix. As illustration, the concrete example of the resonance behavior of scattering and absorption cross sections is studied; this generalizes the well-known results in model exposition. In addition, the fulfilment of the orthodox conditions of micro- and macrocausality for the final results is investigated.

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English version:
Theoretical and Mathematical Physics, 1974, 20:2, 774–781

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Revised: 24.12.1973

Citation: V. S. Ol'khovskii, “Properties of unitary and nonunitary $S$-matrix on the basis of causality and the completeness condition of wave functions”, TMF, 20:2 (1974), 211–222; Theoret. and Math. Phys., 20:2 (1974), 774–781

Citation in format AMSBIB
\Bibitem{Olk74} \by V.~S.~Ol'khovskii \paper Properties of unitary and nonunitary $S$-matrix on the basis of causality and the completeness condition of wave functions \jour TMF \yr 1974 \vol 20 \issue 2 \pages 211--222 \mathnet{http://mi.mathnet.ru/tmf3816} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=468894} \transl \jour Theoret. and Math. Phys. \yr 1974 \vol 20 \issue 2 \pages 774--781 \crossref{https://doi.org/10.1007/BF01037330} 

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• http://mi.mathnet.ru/eng/tmf/v20/i2/p211

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. V. Nikolaev, V. S. Ol'khovskii, “Analytic structure of the $S$ matrix for some classes of potentials”, Theoret. and Math. Phys., 31:2 (1977), 418–421
2. M. Baldo, V. S. Ol'khovskii, “Analytic properties of the $S$-matrix for interactions with Yukawa-potential tails”, Theoret. and Math. Phys., 147:1 (2006), 541–553
3. Olkhovsky V.S., “On the analytic properties of the S-matrix for the unknown interactions surrounded by centrifugal and rapidly decreasing potentials”, Central European Journal of Physics, 9:1 (2011), 13–44
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