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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 2891-2894 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The interelectronic Coulomb interaction between two electrons is expressed in terms of the o(4,2) generators of each electron. The formulation allows an expansion in terms of scaled hydrogenic (also called Sturmian) states of each electron with respect to a common center if the total orbital angular momentum is different from zero. The formulation is exact in the limit where a dimensionless parameter goes to infinity. Numerical evaluation of matrix elements of the interelectronic potential between hydrogenic configurations illustrates the convergence with respect to this parameter.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1965-1970 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The vector model is formulated in a general form that allows its application for calculating square moduli of matrix elements involving continuous bases. The model is applied to positive discrete unitary irreducible representations of SU(1,1) and the classical estimates are compared with the exact results.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 2523-2532 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A relation between representation functions (RF's) of positive discrete unitary irreducible representations (UIR's) of SU(1,1) and the RF's of the UIR's of SU(2) is given. The classical vector model is worked out for the positive discrete UIR's of SU(1,1). Classical domains, probability densities, and algorithms for numerical computations of SU(1,1) RF's and Clebsch–Gordan coefficients are derived, in full analogy with the SU(2) case.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 1079-1089 
    ISSN: 0020-7608
    Keywords: large-order perturbation theory ; lie algebra ; three-body problem ; symbolic computations ; helium atom ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The method of o(4, 2) operator replacements is generalized. As a result, the series whose limiting values when the variable goes to  +∞ should correspond to the two-electron atom energies now have rational coefficients. This generalization allows one also to compute the series for the case of singlet S symmetry, a case which could not be considered in the previous original formulation of the method. Series with rational coefficients for the helium singlet and triplet S ground-state energy are calculated up to order 41 and 45, respectively. Moreover, symbolic computations also allow one to give the first few coefficients of these series for arbitrary values of the nuclear charge Z. Finally, a new method for analytic continuation to the limit  +∞ is presented for the energies of the helium singlet and triplet ground states.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1079-1089, 1997
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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