  For the gravitational Vlasov-Poisson equation, Guo and Rein constructed a
class of classical isotropic states as minimizers of free energies (or
energy-Casimir functionals) under mass constraints. For the quantum
counterpart, that is, the gravitational Hartree equation, isotropic states are
constructed as free energy minimizers by Aki, Dolbeault and Sparber. In this
paper, we are concerned with the correspondence between quantum and classical
isotropic states. Precisely, we prove that as the Planck constant $\hbar$ goes
to zero, free energy minimizers for the Hartree equation converge to those for
the Vlasov-Poisson equation in terms of potential functions as well as via the
Husimi transform and the T\"oplitz quantization.
