Numerical investigation of quasilinearization method in quantum mechanics

R. Krivec*, V. B. Mandelzweig

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

54 Scopus citations

Abstract

The general properties of the quasilinearization method (QLM), particularly its fast convergence, monotonicity and numerical stability are analyzed and verified on the example of scattering length calculations in the variable phase approach to quantum mechanics. The method, whose mathematical basis in physics was discussed recently by one of the present authors (VBM), approximates the solution of a nonlinear differential equation by treating the nonlinear terms as a perturbation about the linear ones, and is not based, unlike perturbation theories, on the existence of some kind of a small parameter. Each approximation of the method sums many orders of the perturbation theory. It is shown that already the first few iterations provide very accurate and numerically stable answers for small and intermediate values of the coupling constant. The number of iterations necessary to reach a given precision only moderately increases for its larger values. The method provides accurate and stable answers for any coupling strengths, including for super singular potentials for which each term of the perturbation theory diverges and the perturbation expansion does not exist even for a very small coupling.

Original languageEnglish
Pages (from-to)69-79
Number of pages11
JournalComputer Physics Communications
Volume138
Issue number1
DOIs
StatePublished - 15 Jul 2001

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