Differential equation for the Uehling potential
Abstract
The second-order differential equation for the Uehling potential is derived explicitly. The right side of this differential equation is a linear combination of the two Macdonald's functions K0(b r) and K1(b r). This central potential is of great interest in many QED problems, since it describes the lowest-order correction for vacuum polarization in few- and many-electron atoms, ions, muonic and bi-muonic atoms/ions as well as in other similar systems.
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