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On the original proof by reductio ad absurdum of the Hohenberg–Kohn theorem for many‐electron Coulomb systems
Author(s) -
Kryachko Eugene S.
Publication year - 2005
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.20539
Subject(s) - reductio ad absurdum , cusp (singularity) , coulomb , analytic proof , quantum mechanics , physics , electron , quantum , theoretical physics , mathematical physics , mathematics , mathematical proof , philosophy , epistemology , geometry , metaphysics
It is shown that, for isolated many‐electron Coulomb systems with Coulombic external potentials, the usual reductio ad absurdum proof of the Hohenberg–Kohn theorem is unsatisfactory since the to‐be‐refuted assumption made about the one‐electron densities and the assumption about the external potentials are not compatible with the Kato cusp condition. The theorem is, however, provable by more sophisticated means, and it is shown here that the Kato cusp condition actually leads to a satisfactory proof. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005