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I got stuck at certain (basic) question regarding Lienard Wiechert (LW) potential of a point charge:

In Heitler's great book "Quantum Theory of Radiation" (I've used the edition from 1954), on page 18, there is a familiar statement that:

[tex]\frac{e}{r}|_{t-r/c}[/tex] is not a valid solution of the retarded potential integral. Heitler justification why this result is wrong is somewhat unclear to me: he states that if "the integral [tex]\int \rho(P',t')dr'[/tex] would not represent the total charge". Does anybody has any idea how the explicit mathematical calculation works in this case or where it could be found ?

I consulted few books (e.g. Jackson, Feynman II, Chapter 20) but only found a derivation of LW potentials (but Feynman nevertheless states, that the above given simple equation is worng, but he also does not give any mathematical justification"

thank you for your kind help