  We propose a new treatment for the quantum three-body problem. It is based on
an expansion of the wave function on harmonic oscillator functions with
different sizes in the Jacobi coordinates. The matrix elements of the
Hamiltonian can be calculated without any approximation and the precision is
restricted only by the dimension of the basis. This method can be applied
whatever the system under consideration. In some cases, the convergence
property is greatly improved in this new scheme as compared to the old
traditional method. Some numerical tricks to reduce computer time are also
presented.
