Probability representation of the quantum evolution and energy-level equations for optical tomograms



The von Neumann evolution equation for the density matrix and the Moyal equation for the Wigner function are mapped onto the evolution equation for the optical tomogram of the quantum state. The connection with the known evolution equation for the symplectic tomogram of the quantum state is clarified. The stationary states corresponding to quantum energy levels are associated with the probability representation of the von Neumann and Moyal equations written for optical tomograms. The classical Liouville equation for optical tomogram is obtained. An example of the parametric oscillator is considered in detail.


evolution equation Moyal equation Wigner function optical tomogram of quantum state classical Liouville equation for optical tomogram 


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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.P. N. Lebedev Physical InstituteRussian Academy of SciencesMoscowRussia

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