Abstract
It is shown that planar quantum dynamics can be related to three-body quantum dynamics in the space of relative motion with a special class of potentials. As an important special case the O(d) symmetry reduction from d degrees of freedom to one degree is presented. A link between two-dimensional (super-integrable) systems and three-body (super-integrable) systems is revealed. As illustration we present number of examples. We demonstrate that the celebrated Calogero–Wolfes three-body potential has a unique property: two-dimensional quantum dynamics coincides with three-body quantum dynamics on the line at d = 1; it is governed by the Tremblay–Turbiner–Winternitz potential for parameter k = 3.
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More From: Journal of Physics A: Mathematical and Theoretical
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