Ядерна фізика та енергетика 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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V. A. Babenko^*, A. V. Nesterov

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

^*Corresponding author. E-mail address: pet2@ukr.net

Abstract: For the quantum quartic anharmonic oscillator with the Hamiltonian H=0.5(p²+x²)+λx⁴ which is one of the classic traditional quantum-mechanical and quantum-field-theory models, its main physical characteristics and properties are thoroughly studied and calculated based on the system's wave function expansion in a complete set of the harmonic oscillator eigenfunctions, i.e., in the basis of eigenfunctions {φ⁽⁰⁾_n} of the unperturbed Hamiltonian H=0.5(p²+x²). Very good convergence of the calculated energy levels of the anharmonic oscillator is demonstrated with respect to the number of basis functions included in the expansion, across a wide range of variation of the parameter λ. Thus, we have computed the energies of the ground and the first six excited states of the system for an exceptionally wide range of the oscillator coupling constant λ. In general, the proposed method provides a very good and accurate way to calculate all system characteristics.

Keywords: anharmonic oscillator, oscillator basis, quantum field theory.

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