Lippmann-Schwinger equation Green functions

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]... [Pg.287]

These properties of the model Green function imply that the Lippmann-Schwinger equation [228],... [Pg.141]

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... [Pg.142]

This multichannel matrix Green function determines a multichannel Lippmann-Schwinger equation... [Pg.144]

The Green function must satisfy boundary conditions at large distances consistent with the wave function i//. The Schrodinger equation can be replaced by an equivalent Lippmann-Schwinger integral equation... [Pg.95]

These two Green functions are related by the Lippmann-Schwinger integral equation... [Pg.121]

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