Title 



Comment on "Breakdown of the HellmannFeynman theorem: Degeneracy is the key"
 
Author 



 
Abstract 



In a recent paper, Zhang and George [Phys. Rev. B 66, 033110 (2002)] have made an application of the HellmannFeynman theorem (HFT) to calculate forces acting on an atom of the buckyball C60 when subjected to small displacement. They noticed inconsistent results (as compared with that by other method) for forces connected with states belonging to a degenerateenergy 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 degeneratelevel 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 systema particle moving in a harmonic confinement, where forces are connected with anisotropic deformation of an isotropic confinement.   
Language 



English
 
Source (journal) 



Physical review : B : condensed matter and materials physics.  Lancaster, Pa, 1998  2015  
Publication 



Lancaster, Pa : 2004
 
ISSN 



10980121 [print]
1550235X [online]
 
Volume/pages 



69:3(2004), p. 15
 
Article Reference 



037103
 
ISI 



000188883800105
 
Medium 



Eonly publicatie
 
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