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Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)

 
 

 

Asymptotics of the spectrum of the hydrogen atom in a magnetic field near the lower boundaries of spectral clusters


Author: A. V. Pereskokov
Translated by: ??
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva.
Journal: Trans. Moscow Math. Soc. 2012, 221-262
MSC (2010): Primary 81R30; Secondary 34Mxx, 81Q20, 33Cxx
DOI: https://doi.org/10.1090/S0077-1554-2013-00205-8
Published electronically: March 21, 2013
MathSciNet review: 3184977
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Abstract: We investigate the second-order Zeeman effect in a magnetic field using irreducible representations of an algebra with the Karasev - Novikova quadratic commutation relations. To each such representation there corresponds a spectral cluster near the energy level of the unperturbed hydrogen atom. Using this model as an example, we describe a general method for constructing asymptotic solutions near the boundaries of spectral clusters based on a new integral representation. We also study the problem of computing quantum averages near the lower boundaries of clusters.


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Additional Information

A. V. Pereskokov
Affiliation: Moscow Power Engineering Institute, Moscow Institute of Electronics and Mathematics of the Higher School of Economics - National Research University
Email: pereskokov62@mail.ru

DOI: https://doi.org/10.1090/S0077-1554-2013-00205-8
Keywords: Operator averaging method, coherent transformation, WKB approximation, turning point, spectral cluster
Published electronically: March 21, 2013
Additional Notes: The author was partially supported by the RFFI (Project 12-01-00627-a), the Ministry of Education and Science of the RF (Contract 14.V37.21.0864), and the Grant Council of the President of the RF (Project NSh-2033.2012.1).
Article copyright: © Copyright 2013 American Mathematical Society

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