The Experts below are selected from a list of 258 Experts worldwide ranked by ideXlab platform

Francisco M Fernandez - One of the best experts on this subject based on the ideXlab platform.

A R Plastino - One of the best experts on this subject based on the ideXlab platform.

N H March - One of the best experts on this subject based on the ideXlab platform.

  • comment on breakdown of the hellmann Feynman Theorem degeneracy is the key
    Physical Review B, 2004
    Co-Authors: Robert Balawender, A Holas, N H March
    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 ${\mathrm{C}}_{60}$ 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.

Hong-yi Fan - One of the best experts on this subject based on the ideXlab platform.

Thomas F George - One of the best experts on this subject based on the ideXlab platform.

  • extended hellmann Feynman Theorem for degenerate eigenstates
    Physical Review B, 2004
    Co-Authors: G P Zhang, Thomas F George
    Abstract:

    In a previous paper, we reported a failure of the traditional Hellmann-Feynman Theorem (HFT) for degenerate eigenstates. This has generated enormous interest among different groups. In four independent papers by Fernandez, by Balawender, Hola, and March, by Vatsya, and by Alon and Cederbaum, an elegant method to solve the problem was devised. The main idea is that one has to construct and diagonalize the force matrix for the degenerate case, and only the eigenforces are well defined. We believe this is an important extension to HFT. Using our previous example for an energy level of fivefold degeneracy, we find that those eigenforces correctly reflect the symmetry of the molecule.

  • breakdown of the hellmann Feynman Theorem degeneracy is the key
    Physical Review B, 2002
    Co-Authors: G P Zhang, Thomas F George
    Abstract:

    The Hellmann-Feynman Theorem is a powerful and popular method to efficiently calculate forces in a variety of dynamical processes, but its validity has rarely been addressed. Here a surprising failure of this Theorem is reported. The forces calculated by the Theorem can be more than fifty times smaller than the forces calculated by the finite differential method. Numerical evidence shows that the energy-level degeneracy is the main reason. An analytical proof reveals that although eigenvalues do not depend on a linear combination of degenerate wave functions, forces do sensitively depend on it, which leads to ill-defined forces. A scheme is proposed to overcome this difficulty.