PERTURBATION EXPANSION OF VARIATIONAL-PRINCIPLES AT ARBITRARY ORDER

When perturbation theory is applied to a quantity for which a variatio nal principle holds (eigenenergies of Hamiltonians, Hartree-Fock or de nsity-functional-theory energy, etc.), different variational perturbat ion theorems can be derived. A general demonstration of the existence of variational principles for an even order of perturbation, when cons traints are present, is provided here. Explicit formulas for these var iational principles for even orders of perturbation, as well as for th e ''2n + 1 theorem,'' to any order of perturbation, with or without co nstraints, are also exhibited. This approach is applied to the case of eigenenergies of quantum-mechanical Hamiltonians, studied previously by other methods.