New summation technique for rapidly divergent perturbation series. Hydrogen atom in magnetic field

DOI10.1063/1.1541119zbMath1061.81028OpenAlexW2018087964MaRDI QIDQ4832923

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Publication date: 14 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1541119

Mathematics Subject Classification ID

Perturbation theories for operators and differential equations in quantum theory (81Q15) Atomic physics (81V45)

Related Items (12)

Mathematical properties of a new Levin-type sequence transformation introduced by Čı́žek, Zamastil, and Skála. I. Algebraic theory ⋮ Study of a generalized Levin-Weniger convergence accelerator of numerical series: Particular cases and applications to multi-electron integrals in atomic physics ⋮ Summation of divergent power series by means of factorial series ⋮ Efficient algorithm for summation of some slowly convergent series ⋮ New properties of a certain method of summation of generalized hypergeometric series ⋮ On the mathematical nature of Guseinov's rearranged one-range addition theorems for Slater-type functions ⋮ Construction of new generalizations of Wynn's epsilon and rho algorithm by solving finite difference equations in the transformation order ⋮ On the choice of \(\beta\) in the \(u\)-transformation for convergence acceleration ⋮ Method of summation of some slowly convergent series ⋮ Development of the Levin-type algorithms for accelerating convergence of sequences ⋮ Convergence analysis of the summation of the factorially divergent Euler series by Padé approximants and the delta transformation ⋮ Large-order behavior of the perturbation energies for the hydrogen atom in magnetic field

Cites Work

• A convergent renormalized strong coupling perturbation expansion for the ground state energy of the quartic, sextic, and octic anharmonic oscillator
• Renormalized perturbation theory for quartic anharmonic oscillator
• Acceleration of Linear and Logarithmic Convergence
• The summation of the ordinary and renormalized perturbation series for the ground state energy of the quartic, sextic, and octic anharmonic oscillators using nonlinear sequence transformations
• Bender–Wu formula for the Zeeman effect
• Development of non-linear transformations for improving convergence of sequences

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