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Projection Methods

  • Chapter
Theory of Resonances

Part of the book series: Reidel Texts in the Mathematical Sciences ((RTMS,volume 3))

Abstract

Projection formalism is a convenient means of studying resonance phenomena arising in scattering and in reactions. It was used for the first time by Feshbach [1] to describe multichannel scattering resonances arising from coupling to closed channels. For this purpose, two mutually orthogonal projectors onto subspaces of open and closed channels are introduced and an energy-dependent effective Hamiltonian is defined in the subspace of the open channels and complex eigenvalues of this Hamiltonian (on the second sheet) determine the location of the resonances. The Feshbach formalism was generalized by Fonda and Newton [2] (see also Chapter 16 of Ref. [3]). After minor modifications projection formalism can also be used to describe potential one-particle resonances [4–7] and, which is of particular importance, many-particle resonances [7].

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Authors and Affiliations

  1. Moscow State University, U.S.S.R.

    V. I. Kukulin & V. M. Krasnopol’sky

  2. Charles University, Prague, Czechoslovakia

    J. Horáček

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  1. V. I. Kukulin
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  2. V. M. Krasnopol’sky
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  3. J. Horáček
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© 1989 V. I. Kukulin, V. M. Krasnopol’sky, J. Horáček

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Kukulin, V.I., Krasnopol’sky, V.M., Horáček, J. (1989). Projection Methods. In: Theory of Resonances. Reidel Texts in the Mathematical Sciences, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7817-2_5

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  • DOI: https://doi.org/10.1007/978-94-015-7817-2_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-8432-3

  • Online ISBN: 978-94-015-7817-2

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