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 Schrödinger 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.

24 pages, no figure, RevTex, Submitted to Phys. Rev. A