  The hyperspherical harmonic (HH) method has been widely applied in recent
times to the study of the bound states, using the Rayleigh-Ritz variational
principle, and of low-energy scattering processes, using the Kohn variational
principle, of A=3 and 4 nuclear systems. When the wave function of the system
is expanded over a sufficiently large set of HH basis functions, containing or
not correlation factors, quite accurate results can be obtained for the
observables of interest. In this paper, the main aspects of the method are
discussed together with its application to the A=3 and 4 nuclear bound and
zero-energy scattering states. Results for a variety of nucleon-nucleon (NN)
and three-nucleon (3N) local or non-local interactions are reported. In
particular, NN and 3N interactions derived in the framework of the chiral
effective field theory and NN potentials from which the high momentum
components have been removed, as recently presented in the literature, are
considered for the first time within the context of the HH method. The purpose
of this paper is two-fold. First, to present a complete description of the HH
method for bound and scattering states, including also detailed formulas for
the computation of the matrix elements of the NN and 3N interactions. Second,
to report accurate results for bound and zero-energy scattering states obtained
with the most commonly used interaction models. These results can be useful for
comparison with those obtained by other techniques and are a significant test
for different future approaches to such problems.
