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International Journal of Theoretical Physics

, Volume 32, Issue 12, pp 2221–2233 | Cite as

Stochastic differential equations anda posteriori states in quantum mechanics

  • A. Barchielli
Article

Abstract

In recent years a consistent theory describing measurements continuous in time in quantum mechanics has been developed. The result of such a measurement is a“trajectory”for one or more quantities observed with continuity in time. Applications are connected especially with detection theory in quantum optics. In such a theory of continuous measurements one can ask what is the state of the system given that a certain trajectory up to timet has been observed. The response to this question is the notion ofa posteriori states and a“filtering”equation governing the evolution of such states: this turns out to be a nonlinear stochastic differential equation for density matrices or for pure vectors. The driving noise appearing in such an equation is not an external one, but its probability law is determined by the system itself (it is the probability measure on the trajectory space given by the theory of continuous measurements).

Keywords

Differential Equation Field Theory Elementary Particle Quantum Field Theory Quantum Mechanic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • A. Barchielli
    • 1
    • 2
  1. 1.Dipartimento di Fisica dell'Università di MilanoMilanItaly
  2. 2.Istituto Nazionale di Fisica NucleareSezione di MilanoMilanItaly

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