What an Effective Criterion of Separability says about the Calogero Type Systems
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In  we have proved a 1-1 correspondence between all separable coordinates on Rn (according to Kalnins and Miller ) and systems of linear PDEs for separable potetials 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.
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TY - JOUR AU - Stefan Rauch-Wojciechowski AU - Claes Waksjö PY - 2005 DA - 2005/01/01 TI - What an Effective Criterion of Separability says about the Calogero Type Systems JO - Journal of Nonlinear Mathematical Physics SP - 535 EP - 547 VL - 12 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2005.12.s1.43 DO - 10.2991/jnmp.2005.12.s1.43 ID - Rauch-Wojciechowski2005 ER -