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Introducing graphical representation

Chapter
Part of the Lecture Notes in Chemistry book series (LNC, volume 42)

Abstract

What does it mean to represent a many-particle model space graphically? It means, that we should be able to identify and label each basis state of that space. For fermionic systems these basis states should be antisymmetric - a very strong requirement, immediately invoking the Pauli principle. Adding spin states |α) and |β) to each orbital state that belongs to Vn we obtain 2n spin-orbital states. These spin-orbital states are ordered and identified in some way, for example
$$|{\phi _1}\rangle = |{\phi _1}\rangle |\alpha \rangle ,|{\overline \phi _1}\rangle = |{\phi _1}\rangle |\beta \rangle ,...|{\phi _n}\rangle ,|{\overline \phi _n}\rangle$$
In the construction of an antisymetric N-particle state at each spin orbital appears at most once, therefore ( N 2n ) spin-orbital configurations or different states are possible, provided that no other restriction than antisymmetry is imposed. Description of a non-symmetric molecule in Born-Oppenheimer approximation requires such states when a strong spin-orbit interaction is present. Graphical representation of the states that do not posses any symmetry other that being antisymmetric (corresponding to determinants) is particularly simple.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • W. Duch
    • 1
    • 2
  1. 1.Max-Planck-Institut für Physik und AstrophysikGarching bei MünchenDeutschland
  2. 2.Instytut FizykiUMKToruńPoland

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