Radon transform on the cylinder and tomography of a particle on the circle

Details Radon transform on the cylinder and tomography of a particle on the circle Radon transform on the cylinder and tomography of a particle on the circle

2007-03-28

arxiv.org/abs/math-ph/0703081v1

Phys. Rev. A 76, 012117 (2007)

Physics

Mathematical Physics

9 pages, 3 figures

Scientific paper

10.1103/PhysRevA.76.012117

The tomographic probability distribution on the phase space (cylinder) related to a circle or an interval is introduced. The explicit relations of the tomographic probability densities and the probability densities on the phase space for the particle motion on a torus are obtained and the relation of the suggested map to the Radon transform on the plane is elucidated. The generalization to the case of a multidimensional torus is elaborated and the geometrical meaning of the tomographic probability densities as marginal distributions on the helix discussed.

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