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Title
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Comment on "Breakdown of the Hellmann-Feynman theorem: Degeneracy is the key"
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Author
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Abstract
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| 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. |
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Language
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English
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Source (journal)
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Physical review : B : condensed matter and materials physics. - Lancaster, Pa, 1998 - 2015
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Publication
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Lancaster, Pa
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2004
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ISSN
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1098-0121
[print]
1550-235X
[online]
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DOI
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10.1103/PHYSREVB.69.037103
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Volume/pages
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69
:3
(2004)
, p. 1-5
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Article Reference
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037103
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ISI
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000188883800105
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Medium
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E-only publicatie
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Full text (Publisher's DOI)
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Full text (open access)
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