The recurrence relations of the angular momentum vector addition coefficients are interpreted as a tight-binding model of a one-dimensional potential. From this model we derive their semi-classical limits in a simple manner, treating separately large J≈L+S and small J≈∣L−S∣. The resulting picture makes their qualitative behavior transparent to beginners, without the use of advanced concepts.
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Sprung et al. (2009) studied this question.