Matrix elements in model spaces

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


So far we have solved kinematical part of our problem, that is we have a convenient graphical description of the many—particle state spaces. Now comes the dynamical part: we want to solve some equations in these spaces. The first step in this direction is to project the operators defined in the infinite dimensional Hilbert space to the finite—dimensional model space (cf Kemble 1958). Thus an operator  = 1 Â1 in M− dimensional space becomes:
$${{\hat{A}}_{M}} = {{1}_{M}}\hat{A}{{1}_{M}} = \sum\limits_{{L = 1}}^{M} {\left| {L\rangle \langle \left. L \right|} \right.} \hat{A}\sum\limits_{{L = 1}}^{M} {\left| {\left. {R\rangle \langle R} \right| = } \right.} \sum\limits_{{L,R = 1}}^{M} {\left| {\left. {L\rangle \langle L} \right|\left. {\hat{A}} \right|R\rangle \langle \left. R \right|} \right.}$$

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

Personalised recommendations