Abstract
A modification of the perturbation theory of a symmetrical anharmonic oscillator is suggested. A more complex zero-order approximation of perturbation theory that considers to a certain degree anharmonicities is chosen rather than a harmonic oscillator model. This approximation is an analog of the self-consistent field model well known in the theory of many-particle systems. A comparison of modified and conventional perturbation theories demonstrates that the modified perturbation theory has much wider applicability range. It can be used for larger values of the parameters at which the conventional perturbation theory becomes inapplicable, namely, for strong anharmonicity and upper energy levels.
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REFERENCES
M. Moshinskii, A Harmonic Oscillator in Modern Physics: from Atoms to Quarks [in Russian], Mir, Moscow (1972).
A. P. Pippard, The Physics of Vibration [Russian translation], Vysshaya Shkola, Moscow (1989).
L. D. Landau and E. M. Lifshits, Quantum Mechanics [in Russian], Nauka, Moscow (1989).
S. Flügge, Practical Quantum Mechanics, Vol. 1 [Russian translation], Mir, Moscow (1974).
Yu. M. Poluéktov, Vestn. Kharkov. Univ., Ser. Fiz., 2 (14), No. 522, 3 (2001).
Yu. M. Poluéktov, <nt>ibid</nt>., 3 (19) No. 569, 3 (2002).
L. D. Landau and E. M. Lifshits, Mechanics [in Russian], Nauka, Moscow (1973).
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Poluéktov, Y.M. Modified Perturbation Theory of an Anharmonic Oscillator. Russian Physics Journal 47, 656–663 (2004). https://doi.org/10.1023/B:RUPJ.0000047847.43927.41
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DOI: https://doi.org/10.1023/B:RUPJ.0000047847.43927.41