Chapter 5
The hyperspherical formalism

Hyperspherical coordinates were introduced by Delves [52] and the formalism of hyperspherical expansion was further developed by many authors [405354] for three-body or more complicated bound states. The usefulness of this method for baryon spectroscopy was shown by several groups [55]. The basic idea is rather simple: the two relative coordinates are merged into a single 6-dimensional vector. The three-body problem in ordinary space becomes equivalent to a two-body problem in 6 dimensions, with a non-central potential. A generalized partial wave expansion leads to an infinite set of coupled radial equations. In practice, however, a very good convergence is achieved with a few partial waves only.

 5.1 Basic formalism
 5.2 The hyperspherical harmonics
 5.3 The radial potentials
 5.4 The coupled equations
 5.5 Results
 5.6 Extension to unequal masses