# Analytic calculation of the edge components of the angular Fock coefficients

@article{Liverts2016AnalyticCO,
title={Analytic calculation of the edge components of the angular Fock coefficients},
author={Evgeny Z. Liverts},
journal={Physical Review A},
year={2016},
volume={94},
pages={022504}
}
• E. Liverts
• Published 5 April 2016
• Mathematics
• Physical Review A
The present paper constitutes a development of our previous work devoted to calculations of the angular Fock coefficients ${\ensuremath{\psi}}_{k,p}(\ensuremath{\alpha},\ensuremath{\theta})$. Explicit analytic representations for the edge components ${\ensuremath{\psi}}_{k,0}^{(0)}$ and ${\ensuremath{\psi}}_{k,0}^{(k)}$ with $k\ensuremath{\le}8$ are derived. The methods developed enable such a calculation for arbitrary $k$. The single-series representation for subcomponent ${\ensuremath{\psi}}_… 4 Citations The Green’s function approach to the Fock expansion calculations of two-electron atoms • Physics • 2018 The renewed Green’s function approach to calculating the angular Fock coefficients, ψk,p(α,θ) is presented. The final formulas are simplified and specified to be applicable for analytical, as well as Electrons on sphere in the helium-like atomic systems The properties of a special configuration of a helium-like atomic system, when both electrons are on the surface of a sphere of radius r, and angle θ characterizes their positions on sphere, are Helium-like atoms. The Green's function approach to the Fock expansion calculations • Physics • 2017 The renewed Green's function approach to calculating the angular Fock coefficients,$\psi_{k,p}(\alpha,\theta)$is presented. The final formulas are simplified and specified to be applicable for Averaged electron densities of the helium-like atomic systems • Physics Journal of Mathematical Physics • 2020 Different kinds of averaging of the wavefunctions/densities of the two-electron atomic systems are investigated. Using several fully three-body methods of variational and direct types, the ground ## References SHOWING 1-10 OF 14 REFERENCES Angular Fock coefficients: Refinement and further development • Mathematics • 2015 The angular coefficients${\ensuremath{\psi}}_{k,p}(\ensuremath{\alpha},\ensuremath{\theta})$of the Fock expansion characterizing the$S\text{-state}$wave function of the two-electron atomic system Schrödinger equation for the helium atom It is shown that the Schr\"odinger equation for the helium atom does not have a Frobenius-type solution in the variables${r}_{1}$,${r}_{2}$, and${r}_{12}\$.
Coordinate systems and analytic expansions for three-body atomic wavefunctions. III. Derivative continuity via solutions to Laplace's equation
• Physics
• 1987
Terms in a few-particle wavefunction, written as an expansion of homogeneous functions, are derived by a method which resembles standard techniques for solving differential equations in one variable.
FOCK EXPANSION FOR THE WAVE FUNCTIONS OF A SYSTEM OF CHARGED PARTICLES
• Physics
• 1959
The method applied by Fock for investigating the wave function of the / sup t/S state of helium is generalized for arbitrary systems of charged particles and for states of any symmetry. (auth)
Premiers termes du développement de Fock pour les états S de Hel et de sa séquence isoélectronique
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Yu
• A. Brychkov and O. I. Marichev, “Integrals and Series. Vol 3. More Special Functions”, Gordon and Breach S. P., New York
• 1986
Coordinate systems and analytic expansions for three-body atomic wavefunctions. I. Partial summation for the Fock expansion in hyperspherical coordinates
• Mathematics
• 1987
A survey of analytic techniques for solving the two-electron atomic Schrodinger equation is presented. The hyperspherical formalism is introduced and specialised to the case of two electrons and zero
Coordinate systems and analytic expansions for three-body atomic wavefunctions. II. Closed form wavefunction to second order in r
• Physics
• 1987
For pt.I, see ibid., vol.20, no.8, p.2043-75 (1987). Several coordinate systems for solving the few-electron Schrodinger equation are presented. Formal solutions corresponding to each coordinate
Convergence properties of Fock's expansion for S-state eigenfunctions of the helium atom
It is proved by functional analytic methods that for S-state solutions of Schrödinger's equation for the helium atom, Fock's expansion in powers of R1/2 and R ln R, where R is the hyperspherical