Convergence properties of the Brillouin--Wigner type of perturbation expansion

Journal Article · Wed Mar 01 04:00:00 EST 1978 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(78)90222-1· OSTI ID:7082758

Leinaas, J M; Kuo, T T.S.

We study the Brillouin--Wigner perturbation expansion of the model-space effective Hamiltonian corresponding to the full Hamiltonian H (x) =H/sub 0/+xH/sub 1/, H/sub 0/+xH/sub 1/, H/sub 0/ and H/sub 1/ being respectively the unperturbed and the interaction Hamiltonian and x being a strength parameter. The radius of convergence for the perturbation expansion is related to the poles of the energy-dependent effective interaction, and the location of these poles in the complex x-plane is discussed. The situation with poles lying off the real x-axis is examined. In terms of the spectrum of the unperturbed Hamiltonian H/sub 0/, some necessary conditions for convergence are derived, and the effects of intruder states are discussed. It is shown that the BW expansion of the ground-state energy can always be made convergent by a shift of the unperturbed energy spectrum.

• Research Organization: Institute of Physics, University of Oslo, Oslo, Norway
• OSTI ID: 7082758
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 111:1; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENVALUES
FUNCTIONS
HAMILTONIAN FUNCTION
INTERACTIONS
PADE APPROXIMATION
PERTURBATION THEORY
RESIDUAL INTERACTIONS
SERIES EXPANSION