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Hellmann–Feynman theorem near the threshold
Author(s) -
Pupyshev Vladimir I.
Publication year - 2002
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.10175
Subject(s) - feynman diagram , hamiltonian (control theory) , wave function , electron , quantum mechanics , limiting , physics , ground state , energy spectrum , continuous spectrum , sequence (biology) , mathematical physics , mathematics , chemistry , mechanical engineering , mathematical optimization , biochemistry , engineering
The features of the spectrum structure are considered for situations where some parameter λ of the N ‐electron Hamiltonian reaches the threshold value η under which the discrete energy level falls into the continuous spectrum. The electron density properties are also studied. It is proved that for a sequence of the wave functions converging in energy to the lower bound of the continuous spectrum as λ approaches η the corresponding sequence of the electron densities converges to the density of the ( N − 1)‐electron ground state. The results generalize the Hellmann–Feynman theorem for the cases where only the one‐side energy derivatives exist or there is no limiting wave function. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002