On the Proof by Reductio ad Absurdum of the Hohenberg-Kohn Theorem for Ensembles of Fractionally Occupied States of Coulomb Systems
نویسنده
چکیده
It is demonstrated that the original reductio ad absurdum proof of the generalization of the Hohenberg-Kohn theorem for ensembles of fractionally occupied states for isolated many-electron Coulomb systems with Coulomb-type external potentials by Gross et al. [Phys. Rev. A 37, 2809 (1988)] is selfcontradictory since the to-be-refuted assumption (negation) regarding the ensemble one-electron densities and the assumption about the external potentials are logically incompatible to each other due to the Kato electron-nuclear cusp theorem. It is however proved that the Kato theorem itself provides a satisfactory proof of this theorem.
منابع مشابه
Absurdum of the Hohenberg - Kohn Theorem for Many - Electron Coulomb Systems
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 so...
متن کاملReply to Comment on " on the Original Proof by Reductio Ad Absurdum of the Hohenberg-kohn Theorem for Many-electron Coulomb Systems "
Any mathematical proof is a game. As a game, it is based on a definite set of rules of logic reasoning which altogether constitutes the subject of logic. One of the simplest rules of the theory of logic is a denial of the truth of a given proposition that is expressed as a sentence. The truth of a proposition has to be denied by asserting its negation. Assuming, for example, that the propositio...
متن کاملReductio ad Absurdum: Planning Proofs by Contradiction
Sometimes it is pragmatically useful to prove a theorem by contradiction rather than finding a direct proof. Some reductio ad absurdum arguments have made mathematical history and the general issue if and how a proof by contradiction can be replaced by a direct proof touches upon deep foundational issues such as the legitimacy of tertium non datur arguments in classical vs. intuitionistic found...
متن کامل5 J ul 2 00 6 1 - Density Operators and Algebraic Version of The Hohenberg - Kohn Theorem
Interrelation of the Coleman's representabilty theory for 1-density operators and abstract algebraic form of the Hohenberg-Kohn theorem is studied in detail. Convenient realization of the Hohenberg-Kohn set of classes of 1-electron operators and the Coleman's set of ensemble representable 1-density operators is presented. Dependence of the Hohenberg-Kohn class structure on the boundary properti...
متن کاملReductio Ad Absurdum and Slippery Slope Arguments: Two Sides of the Same Coin?
Despite the fact that the reductio ad absurdum argument is a valid deductive form, while the slippery slope argument is most often presented as a fallacious form of inductive argument, the two argument types bear some striking similarities. Investigation of these similarities reveals some more universal difficulties in the teaching of informal logic, and, in particular the difference between st...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006