Bender-Wu Formula, the SO(4,2) Dynamical Group, and the Zeeman Effect in Hydrogen

Abstract
Asymptotic formulas are derived for the high-order perturbation coefficients for the hydrogen Zeeman Hamiltonian. The calculation of 100 coefficients in the series for the ground state are also reported. The method of calculation is based on tilting the Hamiltonian by a generator of SO(2, 1) and the algebraization of the problem by means of the dynamical group SO(4,2).