A Most Simple Two-Level System

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


A first example of a two-state quantum system is an ensemble of independent spin-\(\frac{1}{2}\) particles, electrons, for instance, interacting with an external magnetic field via their magnetic dipole moment. We discuss the potential energy of the magnetic dipole interaction and recall the basic experiments that discovered the quantization of energy and angular momentum.


Angular Momentum Magnetic Dipole Moment Zeeman Effect Magnetic Dipole Interaction Magnetic Field Region 
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  1. Mohr, P.J., Taylor, B.N., Newell, D.B.: CODATA recommended values of the fundamental physical constants: 2006. Rev. Mod. Phys. 80, 633 (2008) ADSCrossRefGoogle Scholar

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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