Ŝz—adapted graphs in different forms

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


In this section the full ( N 2n ) dimensional space visualized using G2 (2n: N) graph is decomposed into the subspaces labeled by M S values of Ŝ z operator. To reflect this decomposition the graph has to change its shape. In the Ŝz-adapted space each spin-orbital configuration should have a fixed number sα of α-type spin orbitals and a fixed number s ß of ß-type spin orbitals. In general the number of primitive states ∣φk〉 and ∣\({\bar{\phi }}\) k 〉 should be fixed. The simplest way to achieve it in a graph is to separate the two groups of one-particle states ∣φ k 〉 and ∣\({\bar{\phi }}\) k 〉, placing the first group at the top levels and the second group at the bottom levels of a graph. In this way two subgraphs, the first describing the space of sα particles in ∣k〉 basis and the second representing the space of sß particles in ∣\({\bar{\phi }}\) k 〉 basis, are obtained (Fig 4). The two subgraphs are joined by one vertex.


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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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