  We study the coadjoint orbits of the noncentrally extended (1+1)-affine
Galilei group and compute the relevant Wigner functions built on them
explicitly. We consider the centrally extended (1+1)-Galilei group and study
its coadjoint orbits in the second half of the paper. We also compute the
Wigner functions built on the corresponding coadjoint orbits subsequently.
Finally, a comparative study of the structure of the coadjoint orbits and
corresponding Wigner functions between the extended (1+1)-affine Galilei group
and the centrally extended (1+1)-Galilei group is presented along with possible
physical interpretations.
