The degeneracy problem of a hydrogen atom in a uniform weak magnetic field H is considered from the standpoint of the invariance group that the system obeys. Evidently the degeneracy space has a constant z component of the angular momentum. Under such a classification, the dynamical invariance of the problem is shown to be an isomorph to the Lie group of the linear transformation of the straight line.
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Sadaaki Yanagawa (1973) studied this question.