No abstract

In [15] we have proved a 1-1 correspondence between all separable coordinates on R n (according to Kalnins and Miller [9]) and systems of linear PDEs for separable potentials V (q). These PDEs, after introducing parameters reflecting the freedom of choice of Euclidean reference frame, serve as an effective criterion of separability. This means that any V (q) satisfying these PDEs is separable and that the separation coordinates can be determined explicitly. We apply this criterion to Calogero systems of particles interacting with each other along a line.