Use of Nonlinear Sequence-to-Sequence Transformations in High-Order Perturbation Theory Calculations

Renken, James H.

doi:10.1103/physreva.3.510

Cited by 8 publications

(1 citation statement)

References 4 publications

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“…An iterative approach was used in solving the equations, successful convergence being achieved even in the region of anomalous dispersion by the use of the 6" extrapolation procedures described by Renken (1971) (see also the employment of the Aitken d2 technique in earlier TDHF studies by Alexander andGordon 1972 andStewart 1974). From the solutions of (3) the dynamic polarizability is immediately available as (5).…”

Section: Theory and Numerical Proceduresmentioning

confidence: 99%

Aggregation Effect on the Third-Order Optical Nonlinearity in 4-(N,N-Diethylamino)-β-Nitrostyrene-Doped Polymer Films

Murakami

Morita

Yamashita

et al. 1999

Jpn. J. Appl. Phys.

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Numerical solutions of the time-dependent Hartree-Fock equations are obtained for atoms of the Li and Be isoelectronic sequences for a range of frequencies extending into the continuum. From these excitation energies, bound and continuum oscillator strengths, and derivative properties are computed. The calculated oscillator strength distributions are found generally to be in good agreement with more refined experimental and theoretical estimates.

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Section: Theory and Numerical Proceduresmentioning

confidence: 99%

Aggregation Effect on the Third-Order Optical Nonlinearity in 4-(N,N-Diethylamino)-β-Nitrostyrene-Doped Polymer Films

Murakami

Morita

Yamashita

et al. 1999

Jpn. J. Appl. Phys.

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The Accurate Calculation of Atomic Properties by Numerical Methods

Webster

Jamieson

Stewart

1979

Advances in Atomic and Molecular Physics

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Exact Solutions to the Coupled Hartree-Fock Perturbation Equations

Alexander

Gordon

1972

The Journal of Chemical Physics

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A new method is presented for obtaining exact solutions to the time-dependent coupled Hartree-Fock perturbation equations. We choose an iterative approach, relying on the Aitken δ2 transformation to insure and accelerate convergence. At each iteration the resulting uncoupled inhomogeneous differential equations are solved using the technique previously presented by Alexander and Gordon, based on piecewise polynomial approximation of both the potential and the inhomogeneity. As a numerical application we calculate the frequency-dependent dipole polarizability of the helium atom within the coupled Hartree-Fock approximation. Comparison is made with the results of previous variational and numerical calculations. The method can be extended to the solution of integro-differential equations arising in other areas of chemical physics.

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Use of Nonlinear Sequence-to-Sequence Transformations in High-Order Perturbation Theory Calculations

Cited by 8 publications

References 4 publications

Aggregation Effect on the Third-Order Optical Nonlinearity in 4-(N,N-Diethylamino)-β-Nitrostyrene-Doped Polymer Films

Aggregation Effect on the Third-Order Optical Nonlinearity in 4-(N,N-Diethylamino)-β-Nitrostyrene-Doped Polymer Films

The Accurate Calculation of Atomic Properties by Numerical Methods

Exact Solutions to the Coupled Hartree-Fock Perturbation Equations

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