Perturbative approach to the hydrogen atom in strong magnetic field

The states of hydrogen atom with principal quantum number n <= 3 and zero magnetic quantum number in constant homogeneous magnetic field H are considered. The perturbation theory series is summed with the help of Borel transformation and conformal mapping of the Borel variable. Convergence of approximate energy eigenvalues and their agreement with corresponding existing results are observed for external fields up to n^3 H ~ 5. The possibility of restoring the asymptotic behaviour of energy levels using perturbation theory coefficients is also discussed.