Phys. Rev. A 79, 052116 (2009) [6 pages]Quantization of the Maxwell fish-eye problem and the quantum-classical correspondenceReceived 30 January 2009; published 21 May 2009 The so-called fish-eye model, originally investigated by Maxwell in geometrical optics, is studied both in the classical as well as in the quantum formulations. The best agreement between the two approaches is achieved by using a suitably constructed coherent state, which is of the SU(2) type. The perfect quantum-classical correspondence is obtained in the sense that classical rays go exactly over maxima of the corresponding quantum probability distributions. The distributions are made of linear combinations of the E=0 bound states of the considered model. © 2009 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.79.052116
DOI:
10.1103/PhysRevA.79.052116
PACS:
03.65.Ge, 42.15.Dp, 45.50.Dd
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