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On the quantum anharmonic oscillator and Padé approximations

Authors :
V. A. Babenko
N. M. Petrov
Source :
Âderna Fìzika ta Energetika, Vol 22, Iss 2, Pp 127-142 (2021)
Publication Year :
2021
Publisher :
Institute for Nuclear Research, National Academy of Sciences of Ukraine, 2021.

Abstract

For the quantum quartic anharmonic oscillator with the Hamiltonian H = (p2+x2)/2+λx4, which is one of the traditional quantum-mechanical and quantum-field-theory models, we study summation of its factorially divergent perturbation series by the proposed method of averaging of the corresponding Padé approximants. Thus, for the first time, we are able to construct the Padé-type approximations that possess correct asymptotic behaviour at infinity with a rise of the coupling constant λ. The approach gives very essential theoretical and applicatory-computational advantages in applications of the given method. We also study convergence of the applied approximations and calculate by the proposed method the ground state energy E0(λ) of the anharmonic oscillator for a wide range of variation of the coupling constant λ.

Details

Language :
English, Russian, Ukrainian
ISSN :
1818331X and 20740565
Volume :
22
Issue :
2
Database :
Directory of Open Access Journals
Journal :
Âderna Fìzika ta Energetika
Publication Type :
Academic Journal
Accession number :
edsdoj.9159410b166e49cfba1fe14323294251
Document Type :
article
Full Text :
https://doi.org/10.15407/jnpae2021.02.127