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Analysis of a General Theorem Concerning Two Non-Commuting Hermitian Matrices: Quantum Mechanical Implications for Ground and Excited States

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Abstract

A general theorem concerning the spectral relationship of two non-commuting Hermitian matrices is demonstrated. Discussion and analysis of such finding leads to consider its tight connection with respect of the Hohenberg–Kohn theorem (HKT), cornerstone of DFT theory. The present analysis shows that not only HKT can be considered a particular case of the proposed theorem, but also the validity of the studied spectral relationship can be extended from quantum mechanical ground state to excited states as well.

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Authors and Affiliations

  1. Institute of Computational Chemistry, University of Girona, Campus Montilivi, 17071 Girona, Catalonia, Spain

    Ramon Carbó-Dorca

  2. Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S-3), B-9000, Gent, Belgium

    Patrick Bultinck

Authors
  1. Ramon Carbó-Dorca
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  2. Patrick Bultinck
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Correspondence to Ramon Carbó-Dorca.

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Carbó-Dorca, R., Bultinck, P. Analysis of a General Theorem Concerning Two Non-Commuting Hermitian Matrices: Quantum Mechanical Implications for Ground and Excited States. Journal of Mathematical Chemistry 34, 75–82 (2003). https://doi.org/10.1023/A:1025188705395

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  • DOI: https://doi.org/10.1023/A:1025188705395

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