Mass effects in a Three-Body System Bound by Harmonic Oscilators

The problem of three different masses bound by harmonic oscillator potentials is solved exactly. It is shown that Jacobi coordinates cannot, in general, decouple this system into two three-dimensional oscillators but this decoupling can always be obtained in terms of the normal coordinates. The condition for the decoupling in Jacobi coordinates is given. It is shown that the mean distance between each pair of particles depends upon their masses.