P C Abbott and E N Maslen 1987 J. Phys. A: Math. Gen. 20 2043 doi: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
P C Abbott and E N Maslen
Show affiliationsA 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.
- PACS
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03.65.Ge Solutions of wave equations: bound states
31.15.-p Calculations and mathematical techniques in atomic and molecular physics
- MSC
- Subjects
- Dates
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Issue 8 (1 June 1987)
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Coordinate systems and analytic expansions for three-body atomic wavefunctions. I. Partial summation for the Fock expansion in hyperspherical coordinates
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