Separating the degrees of freedom

This leads to the separable Hamiltonian, with the relative motion part given by ($r_{ij}=r$)

$$\hat{H}_r=-\nabla^2_r + \frac{1}{4}\omega^2r^2+ \frac{1}{r},$$

plus a standard Harmonic Oscillator problem for the center-of-mass motion. This system has analytical solutions in two and three dimensions (M. Taut 1993 and 1994).

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