Hydrogen atom in a strong magnetic field: calculation of the energy levels by quantising the normal form of the regularised Kepler Hamiltonian

The energy levels of the hydrogen atom in a magnetic field are obtained by quantising the Birkhoff-Gustavson normal form of the diamagnetically perturbed, regularised Kepler Hamiltonian. The method enables the authors to go beyond the approximations quadratic in the field and to calculate quartic and higher terms in the power expansion for the energy levels. (Only the case m=0 is considered). The result is equivalent to finding the field-dependent third integral of motion.