  The purpose of this paper is to introduce a new way to inquire the quantum
cosmology for a certain gravitational theory. Normally, the quantum
cosmological model is introduced as the minisuperspace theory which is obtained
by reducing the superspace where the Wheel-DeWitt equation is defined on using
the symmetry provided by cosmological principle. Unlike that, the key of our
approach is to reinterpret the cosmology in a classical dynamical way using a
point-like Lagrangian and then quantize the point-like model. We apply the
method into Einstein gravity, gravity with a cosmological constant and the
$f(R)$-gravity, and get their wave equations respectively. By analsysing the
exact solution for the quantum cosmology with and without a cosmological
constant we demonstrate that the cosmological constant is essential and being a
tiny positive number. We also show the possibility of explaining inflation
under the quantum version of cosmology.
