z—adapted graphs

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


Let us consider now a more complicated case of the L̂ z -adapted space. Complications arise from the fact that the orbital momentum projection quantum numbers ml of a single particle take many values ml = 0,±1,±2… while for the spin only two values m s = ±1/2 were possible. Orbitals (primitive states) with different ml values should be represented by arcs of different slopes. There are two parameters demanding careful choice in order to make legible graphs. First, the absolute value of an arc’s slope has to be chosen for the orbital state with a fixed ml value. Second, slopes for the orbitals with ml ± 1 have to be specified. The slope of an arc may be measured by the horizontal distance h m of the two vertices connected by this arc. The slope of an empty arc is most frequently set to zero making the arc vertical. The difference h m — hm−1 should be choosen in such a way that h m is always different from the slope of an empty arc and that each vertex is uniquely labeled by (o, M L ) values.


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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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