Combining stochastic dynamical statevector reduction with spontaneous localization
Abstract
A linear equation of motion for the state vector is presented, in which an antiHermitian Hamiltonian that fluctuates randomly is added to the usual Hamiltonian of the Schrödinger equation. It is shown how the resulting theory describes the continuous evolution of a state vector to an ensemble of reduced state vectors while retaining important physical features of the Ghirardi, Rimini, and Weber [Phys. Rev. D 34, 470 (1986)] theory of spontaneous localization, in which the state vector reduction occurs discontinuously. A novel aspect, compared with ordinary quantum theory, is that the statevector norm changes with time. The squared norm of each state vector is interpreted as being proportional to the probability possessed by that state vector in the ensemble of state vectors. This interpretation is shown to be consistent with the independent Markovian evolution of each state vector.
 Publication:

Physical Review A
 Pub Date:
 March 1989
 DOI:
 10.1103/PhysRevA.39.2277
 Bibcode:
 1989PhRvA..39.2277P
 Keywords:

 03.65.Bz