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Wigner intracule for the Kellner helium‐like ions
Author(s) -
Gill Peter M. W.,
Besley Nicholas A.,
O'Neill Darragh P.
Publication year - 2004
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.20125
Subject(s) - wave function , ion , position and momentum space , helium , quantum mechanics , physics , wigner distribution function , space (punctuation) , electron , atomic physics , fock space , mathematical physics , quantum , philosophy , linguistics
The Kellner wavefunction for a helium‐like ion is the Hartree–Fock solution wherein the orbital is a Slater‐type function with the variationally optimal exponent ζ = Z − 5/16. The Wigner intracule W ( u, v ) of a system gives the joint quasiprobability of finding two electrons whose position space and momentum space separations are | r 1 − r 2 | = u and |p 1 − p 2 | = v , respectively. In this article, we extend Wigner intracule theory beyond Gaussian‐type functions by deriving W ( u, v ) for the Kellner helium‐like ions. Although we have not been able to express W ( u, v ) in closed form, our formulation reduces it to a two‐dimensional integral that can be treated by quadrature. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004