Quantum Dynamical Model for Wave Function Reduction in Classical and Macroscopic Limits

TL;DR

This paper introduces a quantum dynamical model that generalizes existing models to explain wave function collapse during measurement, demonstrating collapse as a natural outcome of Schrödinger evolution in classical and macroscopic limits.

Contribution

It presents a generalized quantum measurement model that unifies exact and approximate solutions, emphasizing the role of Schrödinger evolution factorization in wave packet collapse.

Findings

Wave packet collapse occurs as a consequence of Schrödinger evolution.

The model applies to both exactly solvable and non-solvable cases.

Factorization of Schrödinger evolution is key to understanding wave function collapse.

Abstract

In this papper, 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 macroscopic limit with very large particle number in measuring instrument, this model generally realizes the wave packet collapse in quantum measurement as a consequence of the Schrodinger time evolution in either the exactly-solvable case or the non-(exactly-)solvable case. For the latter, its quasi-adiabatic case is explicitly analysed by making use of the high-order adiabatic approximation method and then manifests the wave packet collapse as well as the exactly-solvable case. By highlighting these analysis, it is finally found that an essence of the dynamical model of wave packet collapse is the factorization of the Schrodinger evolution other than the exact solvability. So many dynamical models including the well-known ones before, which are exactly-solvable or not, can be shown only to be the concrete realizations of this factorizability