Generalized Euler transformation for summing strongly divergent Rayleigh-Schrödinger perturbation series: The Zeeman effect

1983 ◽  
Vol 28 (1) ◽  
pp. 498-501 ◽  
Author(s):  
Jeremiah N. Silverman
Keyword(s):  
Zeeman Effect ◽  
Perturbation Series ◽  
Euler Transformation ◽  
Schrödinger Perturbation

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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