  We show that the solutions of the Wheeler-DeWitt equation in a homogeneous
and isotropic universe are given by triconfluent Heun functions for the
spatially closed, flat, and open geometries of the Friedmann-Robertson-Walker
universe filled with different forms of energy. In a matter-dominated universe,
we find the polynomial solution and the energy density spectrum. In the cases
of radiation-dominated and vacuum universes, there are no polynomial solutions
as shown.
