Symmetries in Quantum Mechanics

  • Walter Greiner
  • Berndt Müller


Symmetries play a fundamental role in physics, and knowledge of their presence in certain problems often simplifies the solution considerably. We illustrate this with the help of three important examples.


Angular Momentum Orbital Angular Momentum Lagrange Function Total Angular Momentum Rotation Group 
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Biographical Notes

  1. NOETHER, Emmy, * Erlangen 23.3.1882, t Bryn Mawr 14.4.1935. N. studied in Göttingen and Erlangen, becoming associate professor in Göt-tingen in 1922. After her emigration to the United States in 1933, she obtained a guest professorship at the the small college of Bryn Mawr. N. has deeply influenced various branches of algebra by her work. It may be ascribed to her influence that structural theoretical thinking became a dominant principle of modern mathematics.Google Scholar
  2. LIE, Sophus, * Nordfjordeid 17.2.1842, † Kristiana (Oslo) 18.2.1899. L. passed his examination as a teacher in Kristiana in 1965. in 1869/1870 he visited Berlin and in 1870, together with Klein, Paris. From 1872 L. was professor in Kristiana, and between 1886/1898 in Leipzig, until he returned to Kristiana as professor in the theory of transformation groups. In Paris L. had perceived the fundamental importance of group theory for mathematical investigations, had discovered tangential transforma-tions and thereby shown that dynamics can be interpreted as a part of group theory. Nearly all his further investigations dealt with the theory continuous transformation groups and their applications.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Walter Greiner
    • 1
  • Berndt Müller
  1. 1.Institut für Theoretische PhysikUniversität FrankfurtFrankfurtFed. Rep. of Germany

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