The meaning of 1 in l(l+1)

The magnitude of the angular momentum ($J^2$) in quantum mechanics is larger than expected from a classical model. We explain this deviation in terms of quantum fluctuations. A standard quantum mechanical calculation gives the correct interpretation of the components of the angular momentum in the vector model in terms of projections and fluctuations. We show that the addition of angular momentum in quantum mechanics gives results consistent with the classical intuition in this vector model.