English
Русский 22-31 p.
In this work, vibrations of a diatomic molecule are considered within the framework of quantum mechanics as an anharmonic oscillator with small values of the anharmonicity coefficient. Based on well-known models of quantum harmonic and anharmonic oscillators, a new model with a variable value of the molecule force constant was created here. The force constant depends on the vibrational quantum number n and the anharmonicity coefficient . Mathematical analysis of this model confirmed its physical validity. As an example, the vibrational energy of an oxygen molecule was calculated within the framework of the model presented in the work.
1. Malyshev L.G., Povzner A.A. Selected chapters of the physics course. Molecular physics and thermodynam-ics: textbook. Ministry of Science and Higher Education. arr. RF. Ekaterinburg: Ural Publishing House. Univ., 2020. P. 14 – 18.
2. Kislov A.N. Nonrelativistic quantum mechanics: textbook. Ministry of Science and Higher Education. educa-tion of the Russian Federation. Ekaterinburg: Ural Publishing House. Univ., 2020. P. 101 – 111.
3. Kislov A.N. Atomic and nuclear physics: textbook. allowance. Ekaterinburg: Ural Publishing House. Univ., 2017. P. 202 – 212.
4. Solomonov V.I., Spirina A.V., Cholah S.O. Optical spectroscopy of atoms, molecules and solids: textbook. Allowance. Ministry of Science and Higher Education of the Russian Federation. Ekaterinburg: Ural Publishing House. Univ., 2021. P. 75 – 78.
5. Komyak A.I. Molecular spectroscopy: a manual. Minsk: BSU, 2015. P. 97.
6. Aleshkevich V.A. General physics course. Molecular physics. M.: FIZMATLIT, 2016. P. 68 – 69.
7. Physical chemistry. Spectrochemistry: laboratory workshop. Ministry of Education and Science of the Russian Federation, Russian Chemical-Technological University named after D.I. Mendeleev; compilers: A.V. Grebennik, A.Yu. Kryukov M.: RKhTU im. D. I. Mendeleeva, 2017. P. 14 – 17.
8. Written D.T. Lecture notes on higher mathematics: a complete course. M.: Iris-press, 2020. P. 151.
9. Vygodsky M.Ya. Handbook of higher mathematics. M: AST Publishing House, 2019. P. 481.
10. Denisov G.S., Tokhadze K.G. Possibilities of the Morse formula in approximating the energy of vibrational levels of a diatomic molecule. Optics and Spectroscopy. 2021. T. 129, issue. 11. P. 1375 – 1381.
11. Ishmukhametov B.Kh., Katsnelson M.I., Polikarpov A.F. Single-electron problems of quantum mechanics in semiclassical consideration: Educational electronic text resource. Ekaterinburg: Ural Publishing House. Univ., 2018. P. 21 – 23.
2. Kislov A.N. Nonrelativistic quantum mechanics: textbook. Ministry of Science and Higher Education. educa-tion of the Russian Federation. Ekaterinburg: Ural Publishing House. Univ., 2020. P. 101 – 111.
3. Kislov A.N. Atomic and nuclear physics: textbook. allowance. Ekaterinburg: Ural Publishing House. Univ., 2017. P. 202 – 212.
4. Solomonov V.I., Spirina A.V., Cholah S.O. Optical spectroscopy of atoms, molecules and solids: textbook. Allowance. Ministry of Science and Higher Education of the Russian Federation. Ekaterinburg: Ural Publishing House. Univ., 2021. P. 75 – 78.
5. Komyak A.I. Molecular spectroscopy: a manual. Minsk: BSU, 2015. P. 97.
6. Aleshkevich V.A. General physics course. Molecular physics. M.: FIZMATLIT, 2016. P. 68 – 69.
7. Physical chemistry. Spectrochemistry: laboratory workshop. Ministry of Education and Science of the Russian Federation, Russian Chemical-Technological University named after D.I. Mendeleev; compilers: A.V. Grebennik, A.Yu. Kryukov M.: RKhTU im. D. I. Mendeleeva, 2017. P. 14 – 17.
8. Written D.T. Lecture notes on higher mathematics: a complete course. M.: Iris-press, 2020. P. 151.
9. Vygodsky M.Ya. Handbook of higher mathematics. M: AST Publishing House, 2019. P. 481.
10. Denisov G.S., Tokhadze K.G. Possibilities of the Morse formula in approximating the energy of vibrational levels of a diatomic molecule. Optics and Spectroscopy. 2021. T. 129, issue. 11. P. 1375 – 1381.
11. Ishmukhametov B.Kh., Katsnelson M.I., Polikarpov A.F. Single-electron problems of quantum mechanics in semiclassical consideration: Educational electronic text resource. Ekaterinburg: Ural Publishing House. Univ., 2018. P. 21 – 23.
Lyakishev V.K., Perfilyev M.S. Quantum model of anharmonic vibrations of a diatomic molecule with a variable force constant and a small value of the anharmonicity coefficient. Chemical Bulletin. 2024. 7 (1). P. 22 – 31. https://doi.org/10.58224/2619-0575-2024-7-1-22-31