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Abstract: The most general coordinates transformations that allow for the exactseparation of the kinetic energy operator of a quantum many-body system intototal center of mass kinetic energy and internal kinetic energy are found anddiscussed. We find i that the suitable transformations, depending on thenumber of particles, have a certain number of free parameters and this allowsfor the generalization of the Jacobi coordinates to a much larger class ofcoordinates with the same properties and ii that there is a new, uncommon,additive group structure hidden in the transformation matrices that isconnected to certain geometric properties of the set of coordinates.



Author: Lorenzo Fortunato

Source: https://arxiv.org/



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