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

Pereskokov, A.

doi:10.1090/S0077-1554-2013-00205-8

Asymptotics of the spectrum of the hydrogen atom in a magnetic field near the lower boundaries of spectral clusters
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by A. V. Pereskokov
Translated by: A. Martsinkovsky

Trans. Moscow Math. Soc. 2012, 221-262

DOI: https://doi.org/10.1090/S0077-1554-2013-00205-8

Published electronically: March 21, 2013

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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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