The results obtained by Pauli, in his article published in 1926 on the hydrogen atom, made essential use of the dynamical so(4) symmetry of the bound states. Pauli used this symmetry to compute the perturbed energy levels of an hydrogen atom in a uniform electric field (Stark effect) and in uniform electric and magnetic fields. While the experimental check of the single Stark effect on the hydrogen atom has been worked out, Pauli's results in mixed fields have been studied only for Rydberg states of rubidium atoms in crossed fields and lithium atoms in parallel fields.
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