ZhETF, Vol. 123,
No. 3,
p. 457 (March 2003)
(English translation - JETP,
Vol. 96, No. 3,
p. 402,
March 2003
available online at www.springer.com
)
PERTURBATIVE APPROACH TO THE HYDROGEN ATOM IN A STRONG MAGNETIC FIELD
Gani V.A., Kudryavtsev A.E., Lensky V.A., Weinberg V.A.
Received: August 15, 2002
PACS: 31.15.Md, 32.60.+i
We consider states of the hydrogen atom with the principal quantum number  and zero magnetic quantum number in a constant homogeneous magnetic field \cH. The perturbation theory series is summed using the Borel transformation and conformal mapping of the Borel variable. Convergence of the approximate energy eigenvalues and their agreement with the corresponding existing results are observed for external fields up to n3\cH / \cH 0\sim 5, where \cH 0 is the atomic magnetic field. The possibility of restoring the asymptotic behavior of energy levels using perturbation theory coefficients is also discussed.
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