Nuclear Physics and Atomic Energy

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Nuclear Physics and Atomic Energy

  ISSN: 1818-331X (Print), 2074-0565 (Online)
  Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine
  Languages: Ukrainian, English
  Periodicity: 4 times per year

  Open access peer reviewed journal

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Nucl. Phys. At. Energy 2021, volume 22, issue 2, pages 127-142.
Section: Nuclear Physics.
Received: 04.11.2020; Accepted: 02.04.2021; Published online: 10.09.2021.
PDF Full text (ua)

On the quantum anharmonic oscillator and Padé approximations

V. A. Babenko*, N. M. Petrov

Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

*Corresponding author. E-mail address:

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.

Keywords: anharmonic oscillator, quantum field theory, perturbation theory, Padé approximants.


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