Radius of convergence of the hole-line expansion and of the Rayleigh-Schrödinger perturbation series in a solvable model

1983 ◽  
Vol 394 (1-2) ◽  
pp. 16-28 ◽  
Author(s):  
Y. Gerstenmaier
Keyword(s):  
Solvable Model ◽  
Perturbation Series ◽  
Radius Of Convergence ◽  
Schrödinger Perturbation

The Validity of Perturbation Series with Zero Radius of Convergence

1966 ◽  
Vol 7 (11) ◽  
pp. 1900-1902 ◽  
Author(s):  
George A. Baker ◽  
Roy Chisholm
Keyword(s):  
Perturbation Series ◽  
Radius Of Convergence ◽  
Zero Radius

Combination of the successive perturbation method with other common methods

1987 ◽  
Vol 65 (5) ◽  
pp. 462-463 ◽  
Author(s):  
V. A. Popescu ◽  
I. M. Popescu
Keyword(s):  
Hydrogen Atom ◽  
Perturbation Method ◽  
Perturbation Series ◽  
Radius Of Convergence ◽  
Fundamental State

For the hydrogen atom in the fundamental state perturbed by βr−1, it is shown how the successive perturbation method can be combined with the method in which some fraction of a nonperturbed term (in the Hamiltonian) is included in the perturbation. Thus, the radius of convergence of the perturbation series is increased.

Analytical expressions for the energies of anharmonic oscillators

2000 ◽  
Vol 78 (9) ◽  
pp. 845-850
Author(s):  
F M Fernández ◽  
R H Tipping
Keyword(s):  
Perturbation Parameter ◽  
Bound State ◽  
Perturbation Series ◽  
Simple Expression ◽  
Branch Points ◽  
Anharmonic Oscillators ◽  
Large Coupling ◽  
Analytical Behavior ◽  
Schrödinger Perturbation ◽  
Analytical Expressions

We propose a systematic construction of algebraic approximants for the bound-state energies of anharmonic oscillators. The approximants are based on the Rayleigh-Schrödinger perturbation series and take into account the analytical behavior of the energies at large values of the perturbation parameter. A simple expression obtained from a low-order perturbation series compares favorably with alternative approximants. Present approximants converge in the large-coupling limit and are suitable for the calculation of the energy of highly excited states. Moreover, we obtain some branch points of the eigenvalues of the anharmonic oscillator as functions of the coupling constant. PACS No.: 03.65Ge

scholarly journals Effect of partitioning on the convergence properties of the Rayleigh-Schrödinger perturbation series

2017 ◽  
Vol 146 (12) ◽  
pp. 124121 ◽  
Author(s):  
Zsuzsanna É. Mihálka ◽  
Ágnes Szabados ◽  
Péter R. Surján
Keyword(s):  
Perturbation Series ◽  
Convergence Properties ◽  
Schrödinger Perturbation

scholarly journals The Rayleigh-Schrödinger perturbation series of quasi-degenerate systems

2011 ◽  
Vol 112 (10) ◽  
pp. 2256-2266 ◽  
Author(s):  
Christian Brouder ◽  
Gérard H.E. Duchamp ◽  
Frédéric Patras ◽  
Gábor Z. Tóth
Keyword(s):  
Perturbation Series ◽  
Schrödinger Perturbation
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