  In a recent paper we proposed and compared various approaches to compute the
ground state and dynamics of the Schr\"{o}dinger--Poisson--Slater (SPS) system
for general external potential and initial condition, concluding that the
methods based on sine pseudospectral discretization in space are the best
candidates. This note is concerned with the case that the external potential
and initial condition are spherically symmetric. For the SPS system with
spherical symmetry, via applying a proper change of variables into the reduced
quasi-1D model we simplify the methods proposed for the general 3D case such
that both the memory and computational load are significantly reduced.
