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

DOI10.1134/S0001434621050102zbMath1467.81047OpenAlexW3180593097MaRDI QIDQ2037725

E. M. Novikova

Publication date: 8 July 2021

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434621050102

zbMATH Keywords

symmetry algebratwisted productquantum averaging methodfrequency resonancecalculus of symbols

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Spinor and twistor methods applied to problems in quantum theory (81R25) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Differential graded algebras and applications (associative algebraic aspects) (16E45) Resonance in context of PDEs (35B34) Ion traps (78A37)

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Semiclassical asymptotics of oscillating tunneling for a quadratic Hamiltonian on the algebra \(\operatorname{su}(1,1)\) ⋮ Magneto-dimensional resonance on curved surfaces

Cites Work

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• Birkhoff-Gustavson normal form in classical and quantum mechanics

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