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Systems and Subsystems, Multiple Particles

  • Brian C. Hall
Chapter
Part of the Graduate Texts in Mathematics book series (GTM, volume 267)

Abstract

Up to this point, we have considered the state of a quantum system to be described by a unit vector in the corresponding Hilbert space, or more properly, an equivalence class of unit vectors under the equivalence relation \(\psi\)e i θ \(\psi\). We will see in this section that this notion of the state of a quantum system is too limited. We will introduce a more general notion of the state of a system, described by a density matrix. The special case in which the system can be described by a unit vector will be called a pure state.

Keywords

Density Matrix Pure State Density Matrice Identical Particle Trace Class 
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.

References

  1. [34].
    M. Reed, B. Simon, Methods of Modern Mathematical Physics. Volume I: Functional Analysis, 2nd edn. (Academic, San Diego, 1980). Volume II: Fourier Analysis, Self-Adjointness (Academic, New York, 1975). Volume III: Scattering Theory (Academic, New York, 1979). Volume IV: Analysis of Operators (Academic, New York, 1978)Google Scholar
  2. [38].
    R.F. Streater, A.S. Wightman, PCT, Spin and Statistics, and All That (Corrected third printing of the 1978 edition). Princeton Landmarks in Physics (Princeton University Press, Princeton, NJ, 2000)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Brian C. Hall
    • 1
  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA

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