Other Tools and Concepts

  • Dirk Dubbers
  • Hans-Jürgen Stöckmann
Part of the Graduate Texts in Physics book series (GTP)


Quantum theory abounds with matrices of different kinds, and often it is not easy to keep track of all this. In this chapter, we introduce some further operators and their matrices, namely the time evolution, rotation, and projection operators. After a digression on pure and mixed quantum states, the density matrix is introduced in an elementary manner and used to derive again some previous results. It is followed by a section on coherences in quantum physics, and a discussion on Dirac’s bra-ket notation.


Density Matrix Pure State Density Operator Pure Spin Transverse Polarization 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dirk Dubbers
    • 1
  • Hans-Jürgen Stöckmann
    • 2
  1. 1.Fak. Physik und Astronomie, Physikalisches InstitutUniversität HeidelbergHeidelbergGermany
  2. 2.Fachbereich Physik Philipps-Universität MarburgMarburgGermany

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