Calculations of infinite series representing higher-order energy corrections for nonrelativistic hydrogen atoms in external fields

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Abstract
A new method is given for the evaluation of higher-order perturbation corrections to energy of the nonrelativistic hydrogen atom in an external field. The choice of a suitable basis in the Hilbert space of bound states for nonrelativistic hydrogen atom is exploited in the method. The infinite series which represents the higher-order energy correction in the Rayleigh-Schrödinger perturbation theory may be expressed in such a basis in terms of finite series which are easily summed. As an illustrative example the summation of a few series, which are of importance for higher-order corrections to energy of the H atom in an external homogeneous magnetic field, is carried out.