  Master equations of the Lindblad type have recently been derived to describe
the dynamics of quarkonium states in the quark-gluon plasma. Because their full
resolution in three dimensions is very challenging, the equations are often
reduced to one dimension. The main ingredient of these equations is the complex
potential that describes the binding of the heavy quark-antiquark pairs and
their interactions with the medium. In this work, we propose a one-dimensional
complex potential parameterized to reproduce at best two key properties -- the
temperature-dependent masses of the eigenstates and their decay widths -- of a
three-dimensional lattice QCD inspired potential. Their spectral decompositions
are calculated to check their compatibility with the positivity of the master
equations.
