Green functions principal value

When the PWCs are orthogonal among themselves (an assumption which is in fact not necessary and that thus far was not made) and to the localized channel, as is the case for the present treatment of the helium atom, the closecoupling ansatz [Eq. (52)] is equivalent to the Lippmann-Schwinger equation with the principal-value Green function [65]... 

Specializing the present derivation to the principal value Green function, the unsymmetrical expression tan = — 2(wo Av f) is exact for an exact solution of the Lippmann-Schwinger equation, but it is not stationary with respect to infinitesimal variations about such a solution. Since w0 = / + G Avf for such a solution, this can be substituted into the unsymmetrical formula to give an alternative, symmetrical expression tan r] = —2(/1 At> + AvG At> /), which is also not stationary. However, these expressions can be combined to define the Schwinger functional... 

The multichannel generalization of the principal value Green function is a linear... 

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