TY - UNPB

T1 - The classical limit of quantum theory

AU - Werner, R. F.

PY - 1995/4/24

Y1 - 1995/4/24

N2 - For a quantum observable A depending on a parameter we define the notion Asbhbar converges in the classical limit. The limits are functions on phase space. Convergence is in norm in the sense that Asbhbar is equivalent with Asbhbar. The wise product of convergent observables converges to the product of the limiting phase space functions. hbar-1 times the commutator of suitable observables converges to the Poisson bracket of the limits. For a large class of convergent Hamiltonians the wise action of the corresponding dynamics on a convergent observable produces a convergent observable, whose limit is computed with the classical Hamiltonian flow generated by the limit of the quantum Hamiltonians. The connections with earlier approaches, based on the WKB method, or on Wigner distribution functions, or on the limits of coherent states are reviewed.

AB - For a quantum observable A depending on a parameter we define the notion Asbhbar converges in the classical limit. The limits are functions on phase space. Convergence is in norm in the sense that Asbhbar is equivalent with Asbhbar. The wise product of convergent observables converges to the product of the limiting phase space functions. hbar-1 times the commutator of suitable observables converges to the Poisson bracket of the limits. For a large class of convergent Hamiltonians the wise action of the corresponding dynamics on a convergent observable produces a convergent observable, whose limit is computed with the classical Hamiltonian flow generated by the limit of the quantum Hamiltonians. The connections with earlier approaches, based on the WKB method, or on Wigner distribution functions, or on the limits of coherent states are reviewed.

M3 - Preprint

BT - The classical limit of quantum theory

ER -