Abstract
For each bounded trajectory of a particle in an arbitrary central field of force there exists a uniformly rotating reference frame in which the trajectory is closed. This circumstance makes it meaningful to introduce a nonconserving analog of the Runge-Lenze vector and to extend the group-theoretical description of the Kepler problem to the general case. In this paper the classical generators obeying theO(4.2)-algebra Poisson-bracket relations are given for the mechanical three-dimensional problem with arbitrary centrally symmetrical potential. A quantization is proposed in which one replaces six classical observables selected among the group generators by the operators obeying the corresponding commutation relations instead of postulating the canonical commutation relations.
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