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We propose a new treatment for the quantum three-body problem. It is based onan expansion of the wave function on harmonic oscillator functions withdifferent sizes in the Jacobi coordinates. The matrix elements of theHamiltonian can be calculated without any approximation and the precision isrestricted only by the dimension of the basis. This method can be appliedwhatever the system under consideration. In some cases, the convergenceproperty is greatly improved in this new scheme as compared to the oldtraditional method. Some numerical tricks to reduce computer time are alsopresented.

Quantum three body problems using harmonic oscillator bases with different sizes