  An improved hyperspherical harmonic method for the quantum three-body problem
is presented to separate three rotational degrees of freedom completely from
the internal ones. In this method, the Schr\"{o}dinger equation of three-body
problem is reduced to a system of linear algebraic equations in terms of the
orthogonal bases of functions. As an important example in quantum mechanics,
the energies and the eigenfunctions of some states of the helium atom and the
helium-like ions are calculated.
