In this last talk, we will turn the tables and discuss the “inverse” to quantization, i.e. the classical limit of quantum mechanics. We will elaborate on a method introduced by Hepp in CMP 1974 for studying the asymptotic behavior of quantum expectations in the limit as Plank’s constant (~) tends to zero. Our goal is to allow for unbounded observables which are (non-commutative) polynomial functions of the position and momentum operators. This is in contrast to Hepp’s original paper where the observables were, roughly speaking, required to be bounded functions of the position and momentum operators. As should be the case, the first order contributions of the quantum expectations come from evaluating the observables along the classical trajectories while the second order “quantum corrections” are computed by evolving the ~ = 1 observables by certain linear canonical transformations. These linear transformations are determined by the degree two pieces of the Taylor expansion of the quantum mechanical Hamiltonian about a classical trajectory.
Downloadable PDF version of the Abstracts.
Further info on Bruce Driver’s Nelder Fellow webpage.