FBS Colloquium Hyperspherical-Harmonics Methods for Few-Body Problems

A review of hyperspherical-harmonics (HH) methods from the standpoint of their applications is given. In the first lecture, the symmetrized and unsymmetrized HH bases and symmetrization methods are presented. The physical obstacles to the straightforward application of the HH expansion are discussed, and expansion acceleration methods are described. In the second lecture, the main HH methods are described, including the correlation function hyperspherical harmonic method (CFHHM), the potential harmonic (PH) methods, and the correlated HH methods (PHH, CHH). The third lecture discusses the advantages and limitations of different HH methods in applications, and compares the results for specific few-body problems obtained by HH methods as well as non-HH methods.