Abstract
The Zeeman—Stark effect for the hydrogen atom in an electromagnetic field is considered by using irreducible representations of an algebra with Karasev—Novikova quadratic commutation relations. The asymptotics of the series of eigenvalues and asymptotic eigenfunctions are obtained near the lower boundaries of the resonance spectral clusters, which are formed near the energy levels of the unperturbed hydrogen atom.
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Acknowledgments
The authors wish to express gratitude to E. M. Novikova for useful discussion of the research results. We also appreciate the significant contribution of the late Mikhail Vladimirovich Karasev to the development of the methods of noncommutative analysis, quantum geometry, and other domains of modern mathematical physics. He attracted our attention to the problem of finding the asymptotics of the spectrum near the boundaries of spectral clusters and always gave us valuable advice.
Funding
The work of A. V. Pereskokov was supported by the Russian Science Foundation under grant 1911-00033.
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Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 5, pp. 734–751.
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Migaeva, A.S., Pereskokov, A.V. Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields near the Lower Boundaries of Spectral Clusters. Math Notes 107, 804–819 (2020). https://doi.org/10.1134/S0001434620050089
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DOI: https://doi.org/10.1134/S0001434620050089