The Greens theorem and function

The most widely used method of solving second-order inhomogeneous differential equations is due to Green. Because it is formal, it is easily adapted to many situations. For the diffusion of an ion-pair under the influence of an interaction energy U, the diffusion equation for the density at r, t, given that the ion-pair was formed at r0, f0, is given by [cf. eqn. (316)] 

Compare this with eqn. (141). The Green s function, G(r, t r0, f0), is closely related to p, as it satisfies the equation 

The equation should be compared with eqn, (318). When the boundary and initial conditions which the Green s function has to satisfy are chosen to be the same as those satisfied by e p, the problem reduces to finding the Green s function and evaluating the third term on the right-hand side of eqn. (320). 

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