Hellmann-feynman theorem at degeneracies

Ofir Alon, S. Cederbaum

Research output: Contribution to journalArticlepeer-review


The Hellmann-Feynman theorem is extended to account for degenerate states. Given a point λ=λ0 in parameter space where the energy E(λ0) is n-fold degenerate, it is shown that the corresponding n forces (slopes) are obtained by diagonalizing the derivative of the Hamiltonian, -∂H(λ)/∂λ|λ=λ0, in the subspace of degenerate eigenstates. Such a rotation within the subspace of degenerate eigenfunctions is easy and simple to apply in practical calculations and should be performed separately for each independent direction in parameter space for which the forces are to be calculated.

Original languageEnglish
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number11
StatePublished - 15 Jul 2003
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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