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So far authors have only treated the (Formula presented) case, ignoring the problems of higher angular momenta. In principle, they can be treated in the PO formalism but parameters for the angular momentum couplings are difficult to calculate directly and difficult to model as well. See, e.g., W. Domcke and C. Mündel, J. Phys. B 18, 4491 (1985)
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The vectors (Formula presented) may be understood as elements of a composite Hilbert space Y that is a direct sum of the (Formula presented)-particle space and the dual space of the (Formula presented)-particle space (Formula presented) where N is the number of electrons of the target molecule. The primary space, which is spanned by the composite states (Formula presented) is only a (small) subspace of Y. The secondary space is defined by the orthogonal complement of the primary space in Y
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The vectors (Formula presented) may be understood as elements of a composite Hilbert space Y that is a direct sum of the (Formula presented)-particle space and the dual space of the (Formula presented)-particle space (Formula presented) where N is the number of electrons of the target molecule. The primary space, which is spanned by the composite states (Formula presented) is only a (small) subspace of Y. The secondary space is defined by the orthogonal complement of the primary space in Y.
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48
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85037213560
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The present derivation of Dyson’s equation can also be formulated without reference to a particular basis of the primary or secondary space with the help of projection operators analogous to the derivation of the optical potential in Sec. IV C (see Ref
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The present derivation of Dyson’s equation can also be formulated without reference to a particular basis of the primary or secondary space with the help of projection operators analogous to the derivation of the optical potential in Sec. IV C (see Ref. 43). The R dependence of the projection operators is well defined and derives only from the electronic ground state (Formula presented)
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