Angular Momentum Coupling

  • Jouni Suhonen
Part of the Theoretical and Mathematical Physics book series (TMP)


In nuclear physics, as also in atomic and molecular physics, the entities to be described consist of sub-entities with some orbital angular momentum and spin. The angular momentum of the entity is built, then, of the angular momenta of the sub-entities. This building process leads to quantum-mechanical angular momentum coupling. This chapter presents the basic machinery for treating angular momentum and its coupling. Clebsch-Gordan coefficients and 3j symbols are introduced. It is shown that Clebsch-Gordan coefficients and 3j symbols relate to the coupling of two angular momenta. Increasing the number of angular momenta to be coupled leads to more complicated coupling patterns. Transformations between different coupling schemes are mediated by 6j symbols and 9j symbols, relating to the coupling of three and four angular momenta respectively. A host of special relations and special cases are listed to make the manipulations of angular momentum algebra easier and more straightforward in the physical applications of the chapters to come.


Angular Momentum Quantum Number Orbital Angular Momentum Total Angular Momentum Coupling Scheme 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jouni Suhonen
    • 1
  1. 1.Department of PhysicsUniversity of JyväskyläJyväskyläFinland

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