### 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 language | English |
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Pages (from-to) | 105-120 |

Number of pages | 16 |

Journal | Collection of Czechoslovak Chemical Communications |

Volume | 69 |

Issue number | 1 |

Publication status | Published - jan. 2004 |

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### ASJC Scopus subject areas

- Chemistry(all)

### Cite this

**Convergence enhancement in perturbation theory.** / Surján, P.; Szabados, A.

Research output: Article

*Collection of Czechoslovak Chemical Communications*, vol. 69, no. 1, pp. 105-120.

}

TY - JOUR

T1 - Convergence enhancement in perturbation theory

AU - Surján, P.

AU - Szabados, A.

PY - 2004/1

Y1 - 2004/1

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

UR - http://www.scopus.com/inward/record.url?scp=1642288434&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1642288434&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:1642288434

VL - 69

SP - 105

EP - 120

JO - ChemPlusChem

JF - ChemPlusChem

SN - 2192-6506

IS - 1

ER -