Coordinate systems and analytic expansions for three-body atomic wavefunctions. II. Closed form wavefunction to second order in r

J. E. Gottschalk, P. C. Abbott, E. N. Maslen

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

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 system are given in terms of the Fock expansion and their interrelationships and general structure are examined. Attention is focused on the solutions obtained using spherical polar coordinates for a Coulomb potential of arbitrary symmetry. The wavefunction is obtained up to second order in the hyperradius r=(r2 1+r(sup)2 2)12/, and the special case of 1S states is then reduced to a closed form using classical techniques. The insight gained from this reduction suggests methods for solving the wavefunction to all orders. The results hint at the existence of closed form wavefunctions for few-body systems.

Original languageEnglish
Article number024
Pages (from-to)2077-2103
Number of pages27
JournalJournal of Physics A: General Physics
Volume20
Issue number8
DOIs
Publication statusPublished - 1 Dec 1987

Fingerprint

Closed-form
Formal Solutions
polar coordinates
Schrodinger Equation
expansion
Coulomb Potential
Polar coordinates
spherical coordinates
Coulomb potential
Reduction Method
Electron
Symmetry
symmetry
Arbitrary
electrons

Cite this

@article{9b386981fab547608e04da54eb0037ba,
title = "Coordinate systems and analytic expansions for three-body atomic wavefunctions. II. Closed form wavefunction to second order in r",
abstract = "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 system are given in terms of the Fock expansion and their interrelationships and general structure are examined. Attention is focused on the solutions obtained using spherical polar coordinates for a Coulomb potential of arbitrary symmetry. The wavefunction is obtained up to second order in the hyperradius r=(r2 1+r(sup)2 2)12/, and the special case of 1S states is then reduced to a closed form using classical techniques. The insight gained from this reduction suggests methods for solving the wavefunction to all orders. The results hint at the existence of closed form wavefunctions for few-body systems.",
author = "Gottschalk, {J. E.} and Abbott, {P. C.} and Maslen, {E. N.}",
year = "1987",
month = "12",
day = "1",
doi = "10.1088/0305-4470/20/8/024",
language = "English",
volume = "20",
pages = "2077--2103",
journal = "Journal of Physics A: Mathematical and General",
issn = "0305-4470",
publisher = "IOP Publishing - Europhysics Letters",
number = "8",

}

Coordinate systems and analytic expansions for three-body atomic wavefunctions. II. Closed form wavefunction to second order in r. / Gottschalk, J. E.; Abbott, P. C.; Maslen, E. N.

In: Journal of Physics A: General Physics, Vol. 20, No. 8, 024, 01.12.1987, p. 2077-2103.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Coordinate systems and analytic expansions for three-body atomic wavefunctions. II. Closed form wavefunction to second order in r

AU - Gottschalk, J. E.

AU - Abbott, P. C.

AU - Maslen, E. N.

PY - 1987/12/1

Y1 - 1987/12/1

N2 - 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 system are given in terms of the Fock expansion and their interrelationships and general structure are examined. Attention is focused on the solutions obtained using spherical polar coordinates for a Coulomb potential of arbitrary symmetry. The wavefunction is obtained up to second order in the hyperradius r=(r2 1+r(sup)2 2)12/, and the special case of 1S states is then reduced to a closed form using classical techniques. The insight gained from this reduction suggests methods for solving the wavefunction to all orders. The results hint at the existence of closed form wavefunctions for few-body systems.

AB - 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 system are given in terms of the Fock expansion and their interrelationships and general structure are examined. Attention is focused on the solutions obtained using spherical polar coordinates for a Coulomb potential of arbitrary symmetry. The wavefunction is obtained up to second order in the hyperradius r=(r2 1+r(sup)2 2)12/, and the special case of 1S states is then reduced to a closed form using classical techniques. The insight gained from this reduction suggests methods for solving the wavefunction to all orders. The results hint at the existence of closed form wavefunctions for few-body systems.

UR - http://www.scopus.com/inward/record.url?scp=0001489643&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/20/8/024

DO - 10.1088/0305-4470/20/8/024

M3 - Article

VL - 20

SP - 2077

EP - 2103

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 8

M1 - 024

ER -