Quantum Theory for Mathematicians pp 419-440 | Cite as

# Systems and Subsystems, Multiple Particles

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## 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
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## References

- [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 - [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

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