Asymptotic approximations to Clebsch-Gordan coefficients from a tight-binding model

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.