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Matrix elements in the Ŝz and L̂z-adapted spaces

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

Abstract

Calculation of matrix elements in the Ŝ z -adapted space will serve as a simple application of the previous paragraph’s general formalism. It will also serve as a preparation for more complex applications discussed in the next sections. In Ŝ z -adapted case ❘L, ∑〉 in Eq (2.37) represents a determinant, ❘L〉 designating the orbital product and ❘∑〉 the product of α,β spin functions corresponding to these orbitals. The orbital configurations are represented by the three-slope graph (cf Fig 7, 8, 32) and the primitive spin functions by the M-diagram (Fig 9). Alternatively, the ❘L,∑〉 states are represented by non-fagot graphs (cf Fig 48). The elements 〈L̂∑❘Ô❘RΘ〉 may be obtained directly from these graphs (Duch 1985c) analyzing the paths corresponding to ❘L, ∑〉 and ❘R,Θ〉. Let us start from analysis of the three-slope graph and the associated M-diagrams. Purely graphical method is presented first, with a more direct and computationally attractive approach evolving from it. The use of the four-slope and other non-fagot graphs is discussed later in this section. Because the L̂ z and (L̂ z z -adapted spaces have also determinantal bases the same techniques as for Ŝ z eigenfunctions are applicable.

Keywords

Matrix Element Shift Operator Orbital Configuration Occupied Orbital Loop Body 
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

© 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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