  The hyperspherical harmonic basis is used to describe bound states in an
$A$--body system. The approach presented here is based on the representation of
the potential energy in terms of hyperspherical harmonic functions. Using this
representation, the matrix elements between the basis elements are simple, and
the potential energy is presented in a compact form, well suited for numerical
implementation. The basis is neither symmetrized nor antisymmetrized, as
required in the case of identical particles; however, after the diagonalization
of the Hamiltonian matrix, the eigenvectors reflect the symmetries present in
it, and the identification of the physical states is possible, as it will be
shown in specific cases. We have in mind applications to atomic, molecular, and
nuclear few-body systems in which symmetry breaking terms are present in the
Hamiltonian; their inclusion is straightforward in the present method. As an
example we solve the case of three and four particles interacting through a
short-range central interaction and Coulomb potential.
