Measurability in Linear and NonLinear Quantum Mechanical Systems
Abstract
The measurability by means of continuous measurements, of an observable $\A(t_0)$, at an instant, and of a time averaged observable, $\bar \A=1/T\int \A(t')dt'$, is examined for linear and in particular for nonlinear quantum mechanical systems. We argue that only when the exact (nonperturbative) solution is known, an exact measurement may be possible. A perturbative approach is shown to fail in the nonlinear case for measurements with accuracy $\Delta \bar \A < \Delta \bar \A_{min}(T)$, giving rise to a restriction on the accuracy. Thus, in order to prepare an initial pure state of a nonlinear system, by means of a continuous measurement, the exact nonperturbative solution must be known.
 Publication:

arXiv eprints
 Pub Date:
 April 1997
 DOI:
 10.48550/arXiv.quantph/9704001
 arXiv:
 arXiv:quantph/9704001
 Bibcode:
 1997quant.ph..4001A
 Keywords:

 General Relativity and Quantum Cosmology;
 Quantum Physics
 EPrint:
 16 pages, Revtex