Multiconfiguration MC TDHF theory

The variational equations formulated in Section 12.2 may be used to obtain a /nu/ iconfiguration form of the TDHF equations, the generalization being similar to that made in Section 11.9 for a static perturbation. One or two new features appear, however, in the time-dependent case in particular, spedal care is needed in using the Frenkel principle (McWeeny, 1983). We therefore proceed cautiously, writing the principle in the fiiller form (12.2.5a), namely 

It is only when the two terms are linearly independent that it is sufficient to equate each separately to zero, obtaining Frenkel s original form. Orbital variation may be introduced as in Section 8.2 by using 

Changes in W will involve derivatives with respect to both p and p for variations preserving orthonormality, these are not independent, since A must then be anti-Hermitian and hence p = —p, but this constraint may be introduced later. 

The first term in (12.7.1) has already been reduced in deriving (12.2.14) it may now be written in full as 

On introducing the constraints 5p/i=-5pjj, dy=—d, the variation (12.7.4) takes the form 

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