  In the seventies, Lee and Wick proposed an interesting modification of
classical electrodynamics that renders it finite at the quantum level. At the
classical level, this modified theory leads to a regular linear potential at
short distances while also reproducing the Coulomb potential at large
distances. It is shown that a suitable modification of the Lee-Wick idea can
also lead to a linear potential at large distances. For this purpose, we study
an Abelian model that ``simulates" the QCD confining phase while maintaining
the Coulomb behavior at short distances. This paper is organized in three
parts. In the first part, we present a pedagogical derivation of the static
potential in the Lee-Wick model between two heavy test charges using the
Hamiltonian formulation. In the second part, we describe a modification of the
Lee-Wick idea leading to the standard Cornell potential. In the third part, we
consider the effect of replacing a point-like charge with a smeared
Gaussian-type source, that renders the electrostatic potential finite as r-->
0.

General Physics;High Energy Physics - Theory