Convergence enhancement in perturbation theory

Research output: Article

5 Citations (Scopus)

Abstract

The Frobenius norm of operator QW is minimized with respect to level shift parameters applied to the zero-order spectrum, where W is the perturbation while Q is the reduced resolvent of the zero-order Hamiltonian. The stationary condition leads to a simple formula for the level shifts which eliminates degeneracy-induced singularities. Such level shifts may increase the radius of convergence of the perturbation series, and may improve low-order perturbative estimations - as it is found in the cases of a simple matrix eigenvalue problem and the one-dimensional quartic anharmonic oscillator.

Original languageEnglish
Pages (from-to)105-120
Number of pages16
JournalCollection of Czechoslovak Chemical Communications
Volume69
Issue number1
Publication statusPublished - jan. 2004

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ASJC Scopus subject areas

  • Chemistry(all)

Cite this

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title = "Convergence enhancement in perturbation theory",
abstract = "The Frobenius norm of operator QW is minimized with respect to level shift parameters applied to the zero-order spectrum, where W is the perturbation while Q is the reduced resolvent of the zero-order Hamiltonian. The stationary condition leads to a simple formula for the level shifts which eliminates degeneracy-induced singularities. Such level shifts may increase the radius of convergence of the perturbation series, and may improve low-order perturbative estimations - as it is found in the cases of a simple matrix eigenvalue problem and the one-dimensional quartic anharmonic oscillator.",
keywords = "Anharmonic oscillator, Convergence, Hamiltonian, Level shifts, Partitioning, Perturbation theory, Quantum chemistry",
author = "P. Surj{\'a}n and A. Szabados",
year = "2004",
month = "1",
language = "English",
volume = "69",
pages = "105--120",
journal = "ChemPlusChem",
issn = "2192-6506",
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T1 - Convergence enhancement in perturbation theory

AU - Surján, P.

AU - Szabados, A.

PY - 2004/1

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N2 - The Frobenius norm of operator QW is minimized with respect to level shift parameters applied to the zero-order spectrum, where W is the perturbation while Q is the reduced resolvent of the zero-order Hamiltonian. The stationary condition leads to a simple formula for the level shifts which eliminates degeneracy-induced singularities. Such level shifts may increase the radius of convergence of the perturbation series, and may improve low-order perturbative estimations - as it is found in the cases of a simple matrix eigenvalue problem and the one-dimensional quartic anharmonic oscillator.

AB - The Frobenius norm of operator QW is minimized with respect to level shift parameters applied to the zero-order spectrum, where W is the perturbation while Q is the reduced resolvent of the zero-order Hamiltonian. The stationary condition leads to a simple formula for the level shifts which eliminates degeneracy-induced singularities. Such level shifts may increase the radius of convergence of the perturbation series, and may improve low-order perturbative estimations - as it is found in the cases of a simple matrix eigenvalue problem and the one-dimensional quartic anharmonic oscillator.

KW - Anharmonic oscillator

KW - Convergence

KW - Hamiltonian

KW - Level shifts

KW - Partitioning

KW - Perturbation theory

KW - Quantum chemistry

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M3 - Article

VL - 69

SP - 105

EP - 120

JO - ChemPlusChem

JF - ChemPlusChem

SN - 2192-6506

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