Angular Momentum, Spin and Particle Categories

  • Hans Lüth
Part of the Graduate Texts in Physics book series (GTP)


By use of its commutator algebra, properties of the quantum mechanical angular momentum operator are derived. The action of a magnetic field in the Hamilton operator of a single particle is considered and fundamentals of magnetism and the Aharanov–Bohm effect including experimental examples from nanoelectronics are presented. From the Stern–Gerlach experiment the existence of the spin as a further degree of freedom of a particle is concluded. From the discussion of a 2-spin gedanken experiment, the different symmetries of fermion and boson wave functions are derived. Consequences with respect to quantum statistics are treated and the importance for the standard model of elementary particle physics, the periodic table of elements and quantum dots and quantum rings in nanoelectronics is shown.


Wave Function Angular Momentum Quantum Number Hamilton Operator Principal Quantum Number 
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  1. 1.
    R. Resnick, Introduction to Special Relativity (John Wiley and Sons, New York, 2002), p. 157 Google Scholar
  2. 2.
    A. Tonomura, The Quantum World Unveilded by Electron Waves (World Scientific, Singapore, 1998) CrossRefGoogle Scholar
  3. 3.
    Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959) MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    J. Appenzeller, Th. Schäpers, H. Hardtdegen, B. Lengeler, H. Lüth, Phys. Rev. 51, 4336 (1995) ADSCrossRefGoogle Scholar
  5. 5.
    B. Krafft, A. Förster, A. van der Hart, Th. Schäpers, Physica E 9, 635 (2001) ADSCrossRefGoogle Scholar
  6. 6.
    I. Estermann, Recent research in molecular beams, in A Collection of Papers Dedicated to Otto Stern, ed. by I. Estermann (Academic Press, New York, 1959) Google Scholar
  7. 7.
    H. Kopfermann, Kernmomente, 2nd edn. (Akademische Verlagsgesellschaft, Frankfurt, 1956) zbMATHGoogle Scholar
  8. 8.
    T.E. Phipps, J.B. Taylor, Phys. Rev. 29, 309 (1927) ADSCrossRefGoogle Scholar
  9. 9.
    Ch. Berger, Elementarteilchenphysik – Von den Grundlagen zu den modernen Experimenten (Springer, Berlin, 2006) Google Scholar
  10. 10.
    C.D. Anderson, Phys. Rev. 43, 491 (1933) ADSCrossRefGoogle Scholar
  11. 11.
    L.P. Kouwenhoven, D.G. Austing, S. Tarucha, Rep. Prog. Phys. 64, 701 (2001) ADSCrossRefGoogle Scholar
  12. 12.
    H. Haken, H.C. Wolf, Atom- und Quantenphysik (Springer, Berlin, 1980), p. 153 CrossRefGoogle Scholar
  13. 13.
    A. Fuhrer, S. Lüscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider, M. Bichler, Nature 412, 822 (2001) ADSCrossRefGoogle Scholar
  14. 14.
    F. Schwabl, Quantenmechanik, 2nd edn. (Springer, Berlin, 1990), pp. 104–105 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hans Lüth
    • 1
  1. 1.Forschungszentrum Jülich GmbH, Peter Grünberg Institut (PGI)PGI-9: Semiconductor Nanoelectronics and Jülich Aachen Research Alliance (JARA)JülichGermany

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