Group Representations in Quantum Mechanics

Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 78)


This chapter presents fundamentals required in applications of group theory to quantum-mechanical problems. Physical systems considered in quantum mechanics, in general, possess some symmetry, and the symmetry is reflected in the Hamiltonian of the system. As a result, eigenfunctions of the Hamiltonian will have certain transformation properties. These symmetry considerations are facilitated by explicit use of the concepts of groups and representations. In addition, group theory is powerful in discussing energy level splitting due to perturbation and in deriving various selection rules.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  1. 1.Japan Women’s UniversityBunkyo-ku, Tokyo 112Japan
  2. 2.Department of Physics, School of Science and TechnologyMeiji UniversityTama-ku, Kawasaki 214Japan

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