Angular Momentum Coherent States

The work of Carruthers & Nieto on the harmonic oscillator coherent states is combined with Schwinger’s construction of angular momentum to produce the angular momentum coherent states. It is shown that these states become the vector representatives of angular momentum in the classical limit, and so are particularly useful for discussing the transition from quantum to classical angular momentum. The uncertainty relations for angle and angular momentum are described and are compatible with the classical limit. Under rotations the coherent states transform in a manner that in the classical limit is equivalent to the transformation of vectors, and in the same limit the root mean square variation of the expectation values of the components of angular momentum become negligible in comparison with the expectation values themselves. The coupling of two angular momenta in the classical limit is investigated: it is shown that although the product of two coherent states is not itself a coherent state, it does represent a packet similar to a true coherent state, and centred on the direction of the classical resultant of the two component vectors. The properties and implications of hyperbolic angular momentum space are discussed.