F. Bopp: "La m'echanique quantique est-elle une m'echanique statistique classique particuli `ere?", Ann.Inst. Henri Poincar'e 15(1956) 81--112 30  Home/Search   Document Not in Database   Summary   Related Articles

....the normalization to unity. This is highly unsatisfactory from the conceptual point of view. Technically it means that operator norms (see (d) above) cannot be estimated without artificial smoothness assumptions [Dau] It is well known that by averaging Wigner functions with a suitable Gaussian [Bop,Car] these difficulties disappear [Dav,Hol,We1] Moreover, the Gaussians can be chosen such that in the classical limit this smearing out becomes negligible anyhow. In their averaged form Wigner functions play an important role in our approach. For a discussion of states that have positive Wigner ....

....value of h) via a classical intermediate step. It is clear that something like this must be possible from the idea that the comparison described by the j hh 0 should be at least asymptotically transitive. Positive maps taking quantum observables to classical ones and conversely are wellknown [Bop,Sim,Dav,Tak,We1] These maps depend on the choice of a normal state, which is usually taken to be coherent, i.e. the ground state of some harmonic oscillator. Let h (x) h) Gammad=4 exp Gammax 2 2h (3:8) be the ground state vector of the standard oscillator Hamiltonian H osc h = ....

F. Bopp: "La m'echanique quantique est-elle une m'echanique statistique classique particuli `ere?", Ann.Inst. Henri Poincar'e 15(1956) 81--112 30

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