DOI: 10.1002/qua.1967.1.6.769. Continued Fractions and Upper and Lower Bounds in the Brillouin‐Wigner Perturbation Scheme

Continued Fractions and Upper and Lower Bounds in the Brillouin‐Wigner Perturbation Scheme

10.1002/qua.1967.1.6.769

Crossref journal-article

Wiley

International Journal of Quantum Chemistry (311)

Abstract

A derivation of approximants to a continued fraction development of the energy is presented. It is based on the techniques of infinite order perturbation theory and inner projection of operators. The approximants have been introduced before; here their formal nature is clarified and conditions under which they exhibit extremal properties are presented. The oscillatory behaviour about the true eigenvalue, observed previously in the Mathieu problem, is explained.Une dérivation des approximations successives pour un développement en fraction continue de l'énergie est presentée. Elle est fondée sur les méthodes de la théorie des perturbations d'ordre infini. Ces approximations sont déjà connues; ici leur nature formelle est clarifiée et des conditions pour qu'ils aient des propietées extrémales sont données. Le comportement oscillatoire autour de la valeur propre exacte, observé auparavant, est expliqué.Es wurde eine Ableitung von Annäherungen einer Entwicklung der Energie in Kettenbrüchen beschrieben. Sie ist auf Methoden der Störungstheorie unendlicher Ordnung gegründet. Diese Annäherungen sind schon früher eingeführt worden; hier wurde ihre formale Natur abgeklärt und Bedingungen, unter welchen sie Extremaleigenschaften besitzen, wurden hergeleitet. Die Schwingungem um den exakten Eigenwert, die früher in dem Mathieuproblem beobachtet worden sind, wurder hier erklärt.

Bibliography

GOSCINSKI, O. (1967). Continued Fractions and Upper and Lower Bounds in the BrillouinâWigner Perturbation Scheme. International Journal of Quantum Chemistry, 1(6), 769â780. Portico.

Authors 1

OSVALDO GOSCINSKI (first)

References 11 Referenced 57

10.1051/jphysrad:01933004010100
{'key': 'e_1_2_1_3_1', 'volume-title': 'Methods of Theoretical Physics', 'author': 'Morse P. M.', 'year': '1953'} / Methods of Theoretical Physics by Morse P. M. (1953)
10.1103/PhysRev.101.1233
10.1103/PhysRev.106.1151
E.Feenberg Mimeographed lecture notes Washington University unpublished.
10.1063/1.1724312
{'key': 'e_1_2_1_8_1', 'volume-title': 'Preprint No. 91, University of Florida Quantum Theory Project', 'author': 'Reid C. E.', 'year': '1966'} / Preprint No. 91, University of Florida Quantum Theory Project by Reid C. E. (1966)
10.1103/PhysRev.139.A357
{'key': 'e_1_2_1_10_1', 'volume-title': 'Perturbation Theory and its Application to Quantum Mechanics', 'author': 'Löwdin P. O.', 'year': '1966'} / Perturbation Theory and its Application to Quantum Mechanics by Löwdin P. O. (1966)
{'key': 'e_1_2_1_11_1', 'volume-title': 'Proceedings of the Symposium on Spectral Theory and Differential Problems, Stillwater, Oklahoma', 'author': 'Aronszajn N.', 'year': '1951'} / Proceedings of the Symposium on Spectral Theory and Differential Problems, Stillwater, Oklahoma by Aronszajn N. (1951)
10.1103/PhysRev.79.469

Dates

Type	When
Created	7 years, 10 months ago (Sept. 29, 2017, 9:59 a.m.)
Deposited	1 year, 10 months ago (Oct. 11, 2023, 6:51 p.m.)
Indexed	1 year, 2 months ago (June 11, 2024, 3:20 p.m.)
Issued	57 years, 9 months ago (Nov. 1, 1967)
Published	57 years, 9 months ago (Nov. 1, 1967)
Published Online	7 years, 11 months ago (Sept. 25, 2017)
Published Print	57 years, 9 months ago (Nov. 1, 1967)

Funders 0

None

BibTeX

@article{GOSCINSKI_1967, title={Continued Fractions and Upper and Lower Bounds in the Brillouin‐Wigner Perturbation Scheme}, volume={1}, ISSN={1097-461X}, url={http://dx.doi.org/10.1002/qua.1967.1.6.769}, DOI={10.1002/qua.1967.1.6.769}, number={6}, journal={International Journal of Quantum Chemistry}, publisher={Wiley}, author={GOSCINSKI, OSVALDO}, year={1967}, month=nov, pages={769–780} }

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