The Stark Effect for a hydrogen atom in a magnetic field

The spectrum of a hydrogen atom in weak perpendicular and parallel electric and magnetic fields is analyzed, with allowance made for diamagnetic interaction. In both cases, the energy spectrum of the highly excited states as a function of the intensity of the electric field given a fixed magnetic field breaks down into three qualitatively different regions. It is noted that this effect can be explained through a quasi-classical analysis of trinomial recurrent relations in which both problems are reduced to solving the relations. The division of the energy spectrum is caused by a rearrangement of states during a change in the ratio of the electric field intensity to the magnetic field intensity; this rearrangement occurs in response to the appearance or disappearance of effective potential barriers. Attention is also given to those aspects of the quasi-classical approximation for trinomial recurrent relations which are required in analyzing the two problems and which have not been discussed in the literature.