The Clebsch-Gordan problem of the angular momentum coherent states

Abstract

The angular momentum coherent states are used to construct a Hilbert space of analytic functions, which is basically a subspace of Bargmann's well-known Hilbert space of analytic functions. The scalar product, the principal vector, and a complete orthonormal set in this Hilbert space are constructed and used for a complete solution of the Clebsch-Gardan problem in the coherent state basis. In this realization the product state is essentially the principal vector and therefore the coupled state itself is the Clebsch-Gordan coefficient.