SOME PROPERTIES OF SYSTEMS WITH QUADRATIC HAMILTONIANS

Marcel Polakovič

   For a quadratic Hamiltonian the classical evolution, the evolution of mean values of quantum position and momentum, classical projection, nonlinear evolution and the projection of quantum evolution by the momentum mapping are investigated. All these evolutions can be, in a sense, regarded as being identical. For some of them the Planck constant is considered to have a varying value.. This leads to the onsideration of a new procedure which is a simple modification of a classical selector. A simulation study suggests that the proposed selector is much more consistent than the classical one.

Keywords: quadratic Hamiltonian, analytic vector, classical projection, nonlinear evolution, momentum mapping

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