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Mathematical Supplement: Fundamental Properties of Lie Groups

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Quantum Mechanics

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Abstract

The rotation group is composed of the infinite number of operators (srtting h=1)

$$ {\hat U_R}\left( {\hat \phi } \right) = \exp \left( { - {\phi _\mu }{{\hat J}_\mu }} \right) = \exp \left( { - i\hat \phi \cdot \hat J} \right). $$
((3.1))

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Biographical Notes

  • CARTAN, Elie Joseph, French mathematician, * 9.4.1869 Dolomien, t 6. 5.1951 Paris, from 1903 professor at Nancy, from 1909 at the Sorbonne. C. was an eminent representative among those who continued and perfected the theory of continuous Lie groups. He worked on differential geometry, differential forms and groups without parameter representation.

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  • CASIMIR, Hendrik Brught Gerhard, Dutch physicist, * 15.7.1909 The Hague, who was the first to work out the quantum mechanics of the rigid rotator. C. in 1942 entered the research laboratory of the Philips B.V. where he became director and in 1957 a member of the board of the company. Besides his early work on the rigid rotator he is known for the Casimir-effect, which is the change of the zero point energy of electromagnetic waves between e.g. two condenser plates.

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  • RACAH, Giulio, * 9.2.1909 Florence, t 28.8.1965 Jerusalem. R. studied at the universities of Florence and Rome as well as at the Eidgenössische Technische Hochschule in Zurich. Later he taught theoretical physics at Florence and Pisa, until he emigrated to Jerusalem in 1939. He continued to be active at the Hebrew University; his main fields of activity were atomic and nuclear physics.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Frankfurt, Robert-Mayer-Str. 8-10, D-6000, Frankfurt, Fed. Rep. of Germany

    Professor Dr. Walter Greiner

Authors
  1. Professor Dr. Walter Greiner
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  2. Professor Dr. Berndt Müller
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© 1989 Springer-Verlag Berlin Heidelberg

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Greiner, W., Müller, B. (1989). Mathematical Supplement: Fundamental Properties of Lie Groups. In: Quantum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-00902-4_3

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  • DOI: https://doi.org/10.1007/978-3-662-00902-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19201-5

  • Online ISBN: 978-3-662-00902-4

  • eBook Packages: Springer Book Archive

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