Perturbation calculation on the hydrogen atom in electric and magnetic fields

A generalization of a perturbation theory without wave function is developed which applies to a hydrogen atom perturbed by magnetic and electric fields. A double perturbation expansion for the Stark–Zeeman effect for parallel fields is considered and results for the states obeying |m| = l = n ? 1 in the zero field limit are presented. Other problems that can be treated this way are discussed.