Time-Dependent Invariants and Green's Functions in the Probability Representation of Quantum Mechanics

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dc.creatorMan'ko, V. I.
dc.creatorRosa, L.
dc.creatorVitale, P.
dc.date1998-02-12
dc.date.accessioned2026-07-07T06:34:09Z
dc.date.available2026-07-07T06:34:09Z
dc.descriptionIn 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 Schrödinger 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.
dc.description29 pages, RevTex, 6 eps-figures, to appear on Phys. Rev. A
dc.identifierhttps://arxiv.org/abs/quant-ph/9802030
dc.identifierhttp://arxiv.org/abs/quant-ph/9802030
dc.identifierPhys.Rev. A57 (1998) 3291
dc.identifierdoi:10.1103/PhysRevA.57.3291
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99434
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.titleTime-Dependent Invariants and Green's Functions in the Probability Representation of Quantum Mechanics
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