### 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 language | English |
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Article number | 023 |

Pages (from-to) | 2043-2075 |

Number of pages | 33 |

Journal | Journal of Physics A: General Physics |

Volume | 20 |

Issue number | 8 |

DOIs | |

Publication status | Published - 1 Dec 1987 |

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*Journal of Physics A: General Physics*,

*20*(8), 2043-2075. [023]. https://doi.org/10.1088/0305-4470/20/8/023

}

*Journal of Physics A: General Physics*, vol. 20, no. 8, 023, pp. 2043-2075. https://doi.org/10.1088/0305-4470/20/8/023

**Coordinate systems and analytic expansions for three-body atomic wavefunctions. I. Partial summation for the Fock expansion in hyperspherical coordinates.** / Abbott, P. C.; Maslen, E. N.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Coordinate systems and analytic expansions for three-body atomic wavefunctions. I. Partial summation for the Fock expansion in hyperspherical coordinates

AU - Abbott, P. C.

AU - Maslen, E. N.

PY - 1987/12/1

Y1 - 1987/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=3843085199&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/20/8/023

DO - 10.1088/0305-4470/20/8/023

M3 - Article

VL - 20

SP - 2043

EP - 2075

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 8

M1 - 023

ER -