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Communications in Mathematical Physics
Article . 1999 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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On the Virial Theorem in Quantum Mechanics

On the virial theorem in quantum mechanics
Authors: Georgescu, V.; Gérard, C.;

On the Virial Theorem in Quantum Mechanics

Abstract

The authors review several versions of the quantum mechanical virial theorem that exist in the literature. By considering an explicits situation, it is shown that the version contained in the book of \textit{H. L. Cycon}, \textit{R. G. Froese}, \textit{W. Kirsch} and \textit{B. Simon} [Schrödinger operators with applications to quantum mechanics and global geometry. Berlin: Springer (1987; Zbl 0619.47005)] is incorrect. In an appendix it is proved a new version of the virial theorem for self-adjoint operators \(A,H\) which only needs the assumption \(e^{isA}{\mathcal D}(|H|^\sigma) \subset{\mathcal D} (|H|^\sigma)\) for some \(\sigma\geq 1/2\) and a certain continuity property of the sesquilinear form associated with the commutator \([A,H]\).

Keywords

virial theorem, Applications of operator theory in the physical sciences, self-adjoint operators, Scattering theory for PDEs, Selfadjoint operator theory in quantum theory, including spectral analysis

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
66
Top 10%
Top 10%
Top 10%
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