Quantum dynamical model for wave-function reduction in classical and macroscopic limits

Abstract

In this paper, a quantum dynamical model describing the quantum-measurement process is presented as an extensive generalization of the Coleman-Hepp model. In both the classical limit with very large quantum number and the macroscopic limit with very large particle number in the measuring instrument, this model generally realizes the wave-packet collapse in quantum measurement as a consequence of the Schr\"odinger time evolution in either the exactly solvable case or the non-exactly-solvable case. For the latter, the quasiadiabatic case is explicitly analyzed by making use of the high-order adiabatic-approximation method, which manifests the wave-packet collapse as well as in the exactly solvable case. By highlighting these analyses, it is finally found that an essence of the dynamical model of wave-packet collapse is the factorization of the Schr\"odinger evolution rather than the exact solvability. Therefore many dynamical models including the previous well-known ones, whether they are exactly solvable or not, can be shown to be only the concrete realizations of this factorizability.