The quartic anharmonic oscillator - an oscillator-basis expansion approach. I. Energy levels study and calculation
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 funct...
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| Format: | Article |
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Institute for Nuclear Research, National Academy of Sciences of Ukraine
2024-09-01
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| Series: | Ядерна фізика та енергетика |
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| Online Access: | https://jnpae.kinr.kyiv.ua/25.3/Articles_PDF/jnpae-2024-25-0216-Babenko.pdf |
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| author | V. A. Babenko A. V. Nesterov |
| author_facet | V. A. Babenko A. V. Nesterov |
| author_sort | V. A. Babenko |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e5015ee759b44bc08a632d558a55ad06 |
| institution | Kabale University |
| issn | 1818-331X 2074-0565 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Institute for Nuclear Research, National Academy of Sciences of Ukraine |
| record_format | Article |
| series | Ядерна фізика та енергетика |
| spelling | doaj-art-e5015ee759b44bc08a632d558a55ad062025-08-20T03:25:02ZengInstitute for Nuclear Research, National Academy of Sciences of UkraineЯдерна фізика та енергетика1818-331X2074-05652024-09-01253216227https://doi.org/10.15407/jnpae2024.03.216The quartic anharmonic oscillator - an oscillator-basis expansion approach. I. Energy levels study and calculationV. A. Babenko0A. V. Nesterov1Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kyiv, UkraineBogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kyiv, UkraineFor 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.https://jnpae.kinr.kyiv.ua/25.3/Articles_PDF/jnpae-2024-25-0216-Babenko.pdfanharmonic oscillatoroscillator basisquantum field theory. |
| spellingShingle | V. A. Babenko A. V. Nesterov The quartic anharmonic oscillator - an oscillator-basis expansion approach. I. Energy levels study and calculation Ядерна фізика та енергетика anharmonic oscillator oscillator basis quantum field theory. |
| title | The quartic anharmonic oscillator - an oscillator-basis expansion approach. I. Energy levels study and calculation |
| title_full | The quartic anharmonic oscillator - an oscillator-basis expansion approach. I. Energy levels study and calculation |
| title_fullStr | The quartic anharmonic oscillator - an oscillator-basis expansion approach. I. Energy levels study and calculation |
| title_full_unstemmed | The quartic anharmonic oscillator - an oscillator-basis expansion approach. I. Energy levels study and calculation |
| title_short | The quartic anharmonic oscillator - an oscillator-basis expansion approach. I. Energy levels study and calculation |
| title_sort | quartic anharmonic oscillator an oscillator basis expansion approach i energy levels study and calculation |
| topic | anharmonic oscillator oscillator basis quantum field theory. |
| url | https://jnpae.kinr.kyiv.ua/25.3/Articles_PDF/jnpae-2024-25-0216-Babenko.pdf |
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