All coordinates transformations that separate the center of mass kinetic energy, their group structure and geometry

Details All coordinates transformations that separate the center of mass kinetic energy, their group structure and geometry All coordinates transformations that separate the center of mass kinetic energy, their group structure and geometry

2009-10-15

arxiv.org/abs/0910.2811v1

J.Phys. A : Math. Theor. 43 (2010) 065301

Physics

Nuclear Physics

Nuclear Theory

Scientific paper

10.1088/1751-8113/43/6/065301

The most general coordinates transformations that allow for the exact separation of the kinetic energy operator of a quantum many-body system into total center of mass kinetic energy and internal kinetic energy are found and discussed. We find i) that the suitable transformations, depending on the number of particles, have a certain number of free parameters and this allows for the generalization of the Jacobi coordinates to a much larger class of coordinates with the same properties and ii) that there is a new, uncommon, additive group structure hidden in the transformation matrices that is connected to certain geometric properties of the set of coordinates.

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