The Density Matrix – A First Approach

  • Ingolf V. Hertel
  • Claus-Peter Schulz
Part of the Graduate Texts in Physics book series (GTP)


Those who want to benefit from reading the next chapter and other advanced text in AMO physics and are not yet familiar with the density matrix, should study the summary given in this chapter with some care. After some introductory remarks we shall start in Sect. 9.1.1 by defining the concept of pure and mixed states. In Sect. 9.1.2 we formally introduce the density operator and in Sect. 9.1.3 its matrix representation which will be illustrated by some simple examples. A general formalism for describing a physical measurement is derived in Sect. 9.2 and applied in Sect. 9.3 to two typical examples. Finally, in Sect. 9.4 we present an introduction to the general theory of radiation from quantum systems in non-isotropic and oriented excited states, based on the formalism developed by Fano and Macek (1973).


Density Matrix Mixed State Pure State Density Operator Excited Atom 
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Acronyms and Terminology


‘Atomic, molecular and optical’, physics.


‘complex conjugate’.


‘electrostatic units’, old system of unities, equivalent to the Gauss system for electric quantities (see Appendix A.3 in Vol. 1).


‘Fine structure’, splitting of atomic and molecular energy levels due to spin orbit interaction and other relativistic effects (Chap.  6 in Vol. 1).


‘Hyperfine structure’, splitting of atomic and molecular energy levels due to interactions of the active electron with the atomic nucleus (Chap.  9 in Vol. 1).


‘Left hand circularly’, polarized light, also σ + light.


‘Right hand circularly’, polarized light, also σ light.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Ingolf V. Hertel
    • 1
  • Claus-Peter Schulz
    • 1
  1. 1.Max-Born-Institut für Nichtlineare Optikund KurzzeitspektroskopieBerlinGermany

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