Geodesic
New Approach to the Procedure of Quantum Averaging for the Hamiltonian of a Resonance Harmonic Oscillator with Polynomial Perturbation for the Example of the Spectral Problem for the Cylindrical Penning Trap
Matematičeskie zametki, Tome 109 (2021) no. 5, pp. 747-767

Voir la notice de l'article provenant de la source Math-Net.Ru

For the perturbed Hamiltonian of a multifrequency resonance harmonic oscillator, a new approach to calculating the coefficients in the procedure of quantum averaging is proposed. The procedure of quantum averaging is transferred to the space of the graded algebra of symbols by using twisted product introduced in the paper. As a result, the averaged Hamiltonian is represented as a function of generators of the quantum symmetry algebra of the harmonic part of the Hamiltonian. The proposed method is applied to the spectral problem for the Hamiltonian of the cylindrical Penning trap.
Keywords: quantum averaging method, calculus of symbols, frequency resonance, twisted product, symmetry algebra. 
@article{MZM_2021_109_5_a7,
     author = {E. M. Novikova},
     title = {New {Approach} to the {Procedure} of {Quantum} {Averaging} for the {Hamiltonian} of a {Resonance} {Harmonic} {Oscillator} with {Polynomial} {Perturbation} for the {Example} of the {Spectral} {Problem} for the {Cylindrical} {Penning} {Trap}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {747--767},
     publisher = {mathdoc},
     volume = {109},
     number = {5},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_5_a7/}
}
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E. M. Novikova. New Approach to the Procedure of Quantum Averaging for the Hamiltonian of a Resonance Harmonic Oscillator with Polynomial Perturbation for the Example of the Spectral Problem for the Cylindrical Penning Trap. Matematičeskie zametki, Tome 109 (2021) no. 5, pp. 747-767. http://geodesic.mathdoc.fr/item/MZM_2021_109_5_a7/