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Resonances The Unifying Route Towards the Formulation of Dynamical Processes Foundations and Applications in Nuclear, Atomic and Molecular Physics pp 475–483Cite as

On a theorem for complex symmetric matrices and its relevance in the study of decay phenomena

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Part of the book series: Lecture Notes in Physics ((LNP,volume 325))

Abstract

The theorem that every square matrix is similar to a symmetric matrix is discussed and its relevance in the quantum mechanical formulation of decay phenomena is emphasized. An alternative proof of the theorem is derived. It is shown that the matrix Cn(0) of order n with elements of the first superdiagonal being 1 and all the remaining ones zero, is similar to q with the elements q kl = exp(iπ(k + 1 - 2)/n)[δkl - 1/n]. The possible occurence of the latter in connection with off diagonal-longe-range-order (ODLRO) is indicated.

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Author information

Authors and Affiliations

  1. Quantum Theory Project Williamson Hall, University of Florida, Gainesville, 32611, Florida, USA

    Charles E. Reid

  2. Quantum Chemistry Group, Uppsala University, Box 518, S-751 20, Uppsala, Sweden

    Erkki Brändas

Authors
  1. Charles E. Reid
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  2. Erkki Brändas
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Erkki Brändas Nils Elander

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© 1989 Springer-Verlag

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Reid, C.E., Brändas, E. (1989). On a theorem for complex symmetric matrices and its relevance in the study of decay phenomena. In: Brändas, E., Elander, N. (eds) Resonances The Unifying Route Towards the Formulation of Dynamical Processes Foundations and Applications in Nuclear, Atomic and Molecular Physics. Lecture Notes in Physics, vol 325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50994-1_54

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  • DOI: https://doi.org/10.1007/3-540-50994-1_54

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50994-3

  • Online ISBN: 978-3-540-46130-2

  • eBook Packages: Springer Book Archive

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