Systems and Subsystems, Multiple Particles

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


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.


Density Matrix Pure State Density Matrice Identical Particle Trace Class 
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  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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