  A dynamical model for the collapse of the wave function in a quantum
measurement process is proposed by considering the interaction of a quantum
system (spin-1/2) with a macroscopic quantum apparatus interacting with an
environment in a dissipative manner. The dissipative interaction leads to
decoherence in the superposition states of the apparatus, making its behaviour
classical in the sense that the density matrix becomes diagonal with time.
Since the apparatus is also interacting with the system, the probabilities of
the diagonal density matrix are determined by the state vector of the system.
We consider a Stern-Gerlach type model, where a spin- 1/2 particle is in an
inhomogeneous magnetic field, the whole set up being in contact with a large
environment. Here we find that the density matrix of the combined system and
apparatus becomes diagonal and the momentum of the particle becomes correlated
with a spin operator, selected by the choice of the system-apparatus
interaction. This allows for a measurement of spin via a momentum measurement
on the particle with associated probabilities in accordance with quantum
principles.
