Coordinate systems and analytic expansions for three-body atomic wavefunctions. I. Partial summation for the Fock expansion in hyperspherical coordinates

P. C. Abbott, E. N. Maslen

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32 Citations (Scopus)

Abstract

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 total angular momentum. Following Fock, the Schrodinger equation is then converted to an infinite set of coupled second-order differential equations by proposing an expansion including logarithmic functions of the interparticle coordinates. The equivalence of the techniques of Pluvinage and Hylleraas (1985) to the Fock expansion is demonstrated and the method for solution is illustrated. The extension to states of arbitrary angular momentum and excited states is indicated. Methods for simplifying the recurrence relation generated by the Fock expansion are used to determine the highest power logarithmic terms to sixth order. Finally, the wavefunction for S states is given to second order as a singly infinite sum of Legendre polynomials.

Original languageEnglish
Article number023
Pages (from-to)2043-2075
Number of pages33
JournalJournal of Physics A: General Physics
Volume20
Issue number8
DOIs
Publication statusPublished - 1 Dec 1987

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Summation
Schrodinger Equation
Angular Momentum
Partial
expansion
Logarithmic
angular momentum
Electron
Infinite sum
Legendre functions
Legendre polynomial
Excited States
Recurrence relation
Second order differential equation
High Power
equivalence
electrons
differential equations
Equivalence
formalism

Cite this

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