Fast convergent quasilinearization approach to quantum problems

R. Krivec; V. B. Mandelzweig

doi:10.1063/1.1932985

Fast convergent quasilinearization approach to quantum problems

R. Krivec^*, V. B. Mandelzweig

^*Corresponding author for this work

Racah Institute of Physics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

Applications of the quasilinearization method (QLM) in physics are discussed. The recent proof of quadratic convergence of the quasilinearization method (QLM), which is valid for almost any potential, is outlined. Numerical results for the Riccati form of the Schrödinger equation illustrate the rapid convergence of QLM. The convergence of QLM is compared with the convergence or lack thereof of the perturbation series and the WKB approximation, which is also found to be a suitable initial approximation for QLM. The rapid convergence then starts much earlier than with simple initial approximations. High precision results of up to 20 decimal places for both the energies and the wave functions are easily obtained.

Original language	English
Title of host publication	FEW-BODY PROBLEMS IN PHYSICS
Subtitle of host publication	The 19th European Conference on Few-Body Problems in Physics
Pages	413-419
Number of pages	7
DOIs	https://doi.org/10.1063/1.1932985
State	Published - 6 May 2005
Event	FEW-BODY PROBLEMS IN PHYSICS: The 19th European Conference on Few-Body Problems in Physics - Groningen, Netherlands Duration: 23 Aug 2004 → 27 Aug 2004

Publication series

Name	AIP Conference Proceedings
Volume	768
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	FEW-BODY PROBLEMS IN PHYSICS: The 19th European Conference on Few-Body Problems in Physics
Country/Territory	Netherlands
City	Groningen
Period	23/08/04 → 27/08/04

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10.1063/1.1932985

Cite this

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title = "Fast convergent quasilinearization approach to quantum problems",

abstract = "Applications of the quasilinearization method (QLM) in physics are discussed. The recent proof of quadratic convergence of the quasilinearization method (QLM), which is valid for almost any potential, is outlined. Numerical results for the Riccati form of the Schr{\"o}dinger equation illustrate the rapid convergence of QLM. The convergence of QLM is compared with the convergence or lack thereof of the perturbation series and the WKB approximation, which is also found to be a suitable initial approximation for QLM. The rapid convergence then starts much earlier than with simple initial approximations. High precision results of up to 20 decimal places for both the energies and the wave functions are easily obtained.",

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Krivec, R & Mandelzweig, VB 2005, Fast convergent quasilinearization approach to quantum problems. in FEW-BODY PROBLEMS IN PHYSICS: The 19th European Conference on Few-Body Problems in Physics. AIP Conference Proceedings, vol. 768, pp. 413-419, FEW-BODY PROBLEMS IN PHYSICS: The 19th European Conference on Few-Body Problems in Physics, Groningen, Netherlands, 23/08/04. https://doi.org/10.1063/1.1932985

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AB - Applications of the quasilinearization method (QLM) in physics are discussed. The recent proof of quadratic convergence of the quasilinearization method (QLM), which is valid for almost any potential, is outlined. Numerical results for the Riccati form of the Schrödinger equation illustrate the rapid convergence of QLM. The convergence of QLM is compared with the convergence or lack thereof of the perturbation series and the WKB approximation, which is also found to be a suitable initial approximation for QLM. The rapid convergence then starts much earlier than with simple initial approximations. High precision results of up to 20 decimal places for both the energies and the wave functions are easily obtained.

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Fast convergent quasilinearization approach to quantum problems

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