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  • 1
    Electronic Resource
    Electronic Resource
    Solution of convergence difficulties in the Madelung-sum problem: An extrapolation scheme for sawtooth sequences (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 349-357 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An extrapolation scheme is presented to handle successfully partial Madelung-sum sequences with zig–zag, both convergent and divergent. Estimates so obtained are found to agree reasonably with the exact results, providing, in cases, even values of superior quality compared to those obtained by invoking the more popular methods of sequence acceleration. The strategy is extremely simple, quite general, and, above all, capable of physically interpreting the limit points in case of divergent sequences. Possibilities of further improvements of the parent scheme are discussed. Remarks on the notion of summability of divergent series in the present context have also been made with a brief analysis. Demonstrative calculations involve a two-dimensional square lattice and a few three-dimensional cubic lattices of practical concern.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529913
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On estimates of the quantum recurrence time (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 84 (1986), S. 3212-3214 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Based on the survival probability, improved estimates of the quantum recurrence time are obtained which desirably respect the scale invariance of the Hamiltonian and reveal roughly an inverse energy-spread dependence. The cases considered correspond to uniform distribution, nonuniform distribution with one dominant term, and the distribution determined perturbatively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.450251
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Limiting behavior of the ratio of 〈r12-1〉 and 〈r1-1〉 in the helium sequence (1981)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 20 (1981), S. 887-889 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The limiting of the 〈r12-1〈/〈r1-1〈 ratio in the He sequence is critically examined at different levels of approximations leading to some interesting results.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560200411
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Variants of Rayleigh-Schrödinger perturbation theory - a new look (1981)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 20 (1981), S. 1273-1284 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Several useful “redefined zero-order Hamiltonian” variants of the Rayleigh-Schrödinger perturbation theory are derived by exploiting the freedom of choice for the orthogonality integral between zero- and first-order wavefunctions. It is found that the more common Hamiltonian repartitioning schemes follow quite naturally, as a consequence of certain consistency requirements. The strategy adopted may as well be employed to derive various newer and profitable zero-order Hamiltonians depending on the nature of the problems. This implication is strengthened by demonstrating the calculational success of one such derived scheme. Feenberg's “scale-changed” Hamiltonian approach is also reinterpreted in the present context.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560200611
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  • 5
    Electronic Resource
    Electronic Resource
    Generalized Euler transformation in extracting useful information from divergent (asymptotic) perturbation series and the construction of Padé approximants (1982)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 307-330 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Euler transformation for accelerating convergence of a series is considered in the context of handling divergent (asymptotically convergent) perturbation series. A generalized (parametrized) version of this transformation is developed, based on the conjecture of Dalgarno and Stewart, which works better. Viewed from this standpoint, the Padé approximants follow as a special case of the parametrized Euler transformation (PET), as is the case with the μ transformation procedure of Feenberg in a perturbative context. The PET is shown to serve as a more general method of handling a divergent series and is able to appreciate the construction and convergence behavior of specific sequences of Padé approximants. The role of parametrization in the context of the Z-1 perturbation theory of atoms is also noted and the workability of the adopted strategy is demonstrated by choosing some specific test cases.
    Additional Material: 8 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560220210
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  • 6
    Electronic Resource
    Electronic Resource
    Feenberg scaling and higher-order invariants in Rayleigh-Schrödinger perturbation theory (1982)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 21 (1982), S. 857-860 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown that the determination of a unique scaling parameter, based on scale-invariant forms for energy in the scaled zero-order Hamiltonian approach of Feenberg, is not possible because the higher-order invariants themselves are nonunique.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560210511
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    Paper (German National Licenses)
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