Physics – Quantum Physics
Scientific paper
1998-02-12
Phys.Rev. A57 (1998) 3291
Physics
Quantum Physics
29 pages, RevTex, 6 eps-figures, to appear on Phys. Rev. A
Scientific paper
10.1103/PhysRevA.57.3291
In the probability representation of quantum mechanics, quantum states are represented by a classical probability distribution, the marginal distribution function (MDF), whose time dependence is governed by a classical evolution equation. We find and explicitly solve, for a wide class of Hamiltonians, new equations for the Green's function of such an equation, the so-called classical propagator. We elucidate the connection of the classical propagator to the quantum propagator for the density matrix and to the Green's function of the Schr\"odinger equation. Within the new description of quantum mechanics we give a definition of coherence solely in terms of properties of the MDF and we test the new definition recovering well known results. As an application, the forced parametric oscillator is considered . Its classical and quantum propagator are found, together with the MDF for coherent and Fock states.
Man'ko Vladimir I.
Rosa Luigi
Vitale Patrizia
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