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Introduction

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Quantum Trajectories and Measurements in Continuous Time

Part of the book series: Lecture Notes in Physics ((LNP,volume 782))

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Quantum mechanics started as a theory of closed systems: the state of the system is a vector of norm one in a Hilbert space and it evolves in time according to the Schrödinger equation (B.11). In order to describe also a possible uncertainty on the initial state, a “statistical” formulation of quantum mechanics has been developed: the states are represented by statistical operators (Sect. B.3.1), also called density matrices, and their evolution is given by the von Neumann equation (B.18). This statistical formulation revealed to be well suited also for open systems. General evolution equations for density operators appeared under the names of master equations and quantum dynamical semigroups [1–5] (Sect. B.3.3); these concepts were generalised and gave rise to the theory of quantum Markov semigroups [6,7].

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  1. Dipto. Matematica, Politecnico di Milano, Piazza Leonarda da Vinci, 32, 20133, Milano, Italy

    Prof. Alberto Barchielli & Dr. Matteo Gregoratti

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Correspondence to Alberto Barchielli .

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Barchielli, A., Gregoratti, M. (2009). Introduction. In: Quantum Trajectories and Measurements in Continuous Time. Lecture Notes in Physics, vol 782. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01298-3_1

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  • DOI: https://doi.org/10.1007/978-3-642-01298-3_1

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