Perturbation expansion of variational principles at arbitrary order

Xavier Gonze

Research output: Contribution to journalArticlepeer-review

220 Citations (Scopus)


When perturbation theory is applied to a quantity for which a variational principle holds (eigenenergies of Hamiltonian, Hartree-Fock or density-functional-theory, etc.), different variation-perturbation theorems can be derived. A general demonstration of the existence of variational principles for an even order of perturbation, when constraints are present, is provided here. Explicit formulas for these variational principles for even orders of perturbation, as well as for the 2n+1 theorem, to any order of perturbation, with or without constraints, are also exhibited. This approach is applied to the case of eigenenergies of quantum-mechanical Hamiltonians, studied previously by other methods.

Original languageEnglish
Pages (from-to)1086-1095
Number of pages10
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number2
Publication statusPublished - 1995
Externally publishedYes


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