A method due to Pechukas (1972) and De Leon and Heller (1984) is used to construct a curvilinear coordinate system appropriate to the first-order quadratic Zeeman effect. The method is introduced through the example of the classical Coulomb problem. The curvilinear nodal coordinates in momentum space are shown to be the elliptical cylindrical (or conical) coordinates employed by Herrick (1982) to separate the diamagnetic Hamiltonian exactly.
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Watanabe et al. (1987) studied this question.