Journal Article10.1023/A:1018852612649
Perturbation method with triangular propagators and anharmonicities of intermediate strength
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TL;DR: In this article, a new flexible version of the Rayleigh-Schrodinger perturbation method was proposed, which admits a lower triangular matrix in place of the usual diagonal unperturbed propagator.
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Abstract: We propose a new, very flexible version of the Rayleigh–Schrodinger perturbation method which admits a lower triangular matrix in place of the usual diagonal unperturbed propagator. The technique and its enhanced efficiency are illustrated on rational anharmonicities V(1)(x)=β×polynomial(x)/polynomial(x). They are shown tractable, in the intermediate coupling regime, as \(\mathcal{O}(\beta {\text{ - }}\beta ^{{\text{(0)}}} )\) perturbations of exact states at non-vanishing β(0)≠0. In this sense our method bridges the gap between the current weak- and strong-coupling expansions.
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Citations
Properties of a class of perturbed Toeplitz periodic tridiagonal matrices
TL;DR: For a class of perturbed Toeplitz periodic tridiagonal (PTPT) matrices, some properties, including the determinant, the inverse matrix, the eigenvalues and the Eigenvectors, are studied in detail.
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A symbolic algorithm for periodic tridiagonal systems of equations
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Theory and algorithm of the inversion method for pentadiagonal matrices
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A novel algorithm for solving quasi penta-diagonal linear systems
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TL;DR: A novel numerical algorithm for solving quasi penta-diagonal linear systems is presented that is less than those of three successful algorithms given by El-Mikkawy and Rahmo, and a new recursive method for inverting the quasi pentanagonal matrices is discussed.
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On the determinant evaluation of quasi penta-diagonal matrices and quasi penta-diagonal Toeplitz matrices
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