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Lie Groups, Quantum Mechanics, Many-Body Theory and Organic Chemistry

  • F. A. Matsen

Abstract

Quantum mechanical perturbation theory provides a realization of the classical Lie groups [1):
  1. i)

    The Hamiltonian is a realization of an element in the covering algebra of the group.

     
  2. ii)

    The zero-order Hamiltonian is an element in the subalgebra spanned by the mutually commuting generators.

     
  3. iii)

    The perturbation Hamiltonian is a function of the “shift” operators.

     
  4. iv)

    The invariant space of the Hamiltonian is a realization of an irreducible subspace of the group space* and the quantum numbers are realizations of the label of the subspace.

     
  5. v)

    The zero-order states are realizations of that basis which is an eigenvector basis to the algebra of the commuting generators.

     

Keywords

Unitary Group Young Diagram Infinitesimal Generator Invariant Space High Weight State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • F. A. Matsen
    • 1
  1. 1.Departments of Physics and ChemistryThe University of TexasAustinUSA

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