The hydrogen atom perturbed by a constant 1-dimensional weak quadratic potential λ z² is solved at first-order perturbation theory using the eigenstates of the total angular momentum operator - the coupled basis. Physical applications of this result could be found, for example, in the study of a quadratic Zeeman effect weaker than fine-structure effects, or in a perturbation caused by instantaneous generalised van der Waals interactions.
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Ríos et al. (2024) studied this question.
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