Title
Comment on "Breakdown of the Hellmann-Feynman theorem: Degeneracy is the key" Comment on "Breakdown of the Hellmann-Feynman theorem: Degeneracy is the key"
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
Lancaster, Pa ,
Subject
Physics
Source (journal)
Physical review : B : condensed matter and materials physics. - Lancaster, Pa, 1998 - 2015
Volume/pages
69(2004) :3 , p. 1-5
ISSN
1098-0121
1550-235X
1098-0121
Article Reference
037103
Carrier
E-only publicatie
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
In a recent paper, Zhang and George [Phys. Rev. B 66, 033110 (2002)] have made an application of the Hellmann-Feynman theorem (HFT) to calculate forces acting on an atom of the buckyball C-60 when subjected to small displacement. They noticed inconsistent results (as compared with that by other method) for forces connected with states belonging to a degenerate-energy level. However a sum of all such HFT forces for a given level was found consistent. Therefore they proposed the average force to be the representative of all forces connected with a degenerate level. Our analysis of these difficulties, based on degenerate perturbation theory, leads to modification of the HFT in application to degenerate-level states. By solving a matrix eigenequation of the extended HFT, as many forces are obtained as degeneracy of the level amounts. The diagonalized matrix involves unperturbed states only. Our considerations are illustrated by a simple system-a particle moving in a harmonic confinement, where forces are connected with anisotropic deformation of an isotropic confinement.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/c5d678/3925.pdf
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