2015/11/08 by Bruce K. Driver, Driver, Bruce K., Pun Wai Tong +1
Mathematics · Physics and Astronomy · #47A63 #81S05 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Primary 81Q20 #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #Secondary 47D08 #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1511.02447
openalex publication_date 2015/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to the study of the classical limit of quantum mechanics. In more detail we will elaborate on a method introduced by Hepp in 1974 for studying the asymptotic behavior of quantum expectations in the limit as Plank's constant (ℏ) 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 expected the leading order contributions of the quantum expectations come from evaluating the observables along the classical trajectories while the next order contributions are computed by evolving the ℏ=1 observables by a linear canonical transformations which is determined by the second order pieces of the quantum mechanical Hamiltonian.