Convergence Enhancement in Perturbation Theory

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Title:Convergence Enhancement in Perturbation Theory
Creators:
Surján, Peter R.
Szabados, Ágnes
Journal or Publication Title:
Collection of Czechoslovak Chemical Communications, 69, 1, pp. 105-120
Uncontrolled Keywords:Anharmonic oscillator, Convergence, Level shifts, Hamiltonian, Partitioning, Perturbation theory, Quantum chemistry

Abstract

The Frobenius norm of operator <i>QW</i> is minimized with respect to level shift parameters applied to the zero-order spectrum, where <i>W</i> is the perturbation while <i>Q</i> 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. <p>

Title:Convergence Enhancement in Perturbation Theory
Creators:
Surján, Peter R.
Szabados, Ágnes
Uncontrolled Keywords:Anharmonic oscillator, Convergence, Level shifts, Hamiltonian, Partitioning, Perturbation theory, Quantum chemistry
Divisions:Life and Chemical Sciences > Institute of Organic Chemistry and Biochemistry > Collection of Czechoslovak Chemical Communications
Journal or Publication Title:Collection of Czechoslovak Chemical Communications
Volume:69
Number:1
Page Range:pp. 105-120
ISSN:0010-0765
E-ISSN:1212-6950
Publisher:Institute of Organic Chemistry and Biochemistry
Related URLs:
URLURL Type
http://dx.doi.org/10.1135/cccc20040105UNSPECIFIED
ID Code:2199
Item Type:Article
Deposited On:06 Feb 2009 17:16
Last Modified:06 Feb 2009 16:16

Citation

Surján, Peter R.; Szabados, Ágnes (2004) Convergence Enhancement in Perturbation Theory. Collection of Czechoslovak Chemical Communications, 69 (1). pp. 105-120. ISSN 0010-0765

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