Noether symmetric minisuperspace model of $f(R)$ cosmology
  We study the metric $f(R)$ cosmology using Noether symmetry approach by
utilizing the behavior of the corresponding Lagrangian under infinitesimal
generators of the desired symmetry. The existence of Noether symmetry of the
cosmological $f(R)$ minisuperspace helps us to find out the form of $f(R)$
function for which such symmetry exist. It is shown that the resulting form for
$f(R)$ yields a power law expansion for the cosmic scale factor. We also show
that in the corresponding Noether symmetric quantum model, the solutions to the
Wheeler-DeWitt equation can be expressed as a superposition of states of the
form $e^{iS}$. It is shown that in terms of such wavefunctions the classical
trajectories can be recovered.
