  We investigate non-linear Schr\"{o}dinger-type formulation of cosmology of
which our cosmological system is a general relativistic FRLW universe
containing canonical scalar field under arbitrary potential and a barotropic
fluid with arbitrary spatial curvatures. We extend the formulation to include
phantom field case and we have found that Schr\"{o}dinger wave function in this
formulation is generally non-normalizable. Assuming power-law expansion, $a
\sim t^q$, we obtain scalar field potential as function of time. The
corresponding quantities in Schr\"{o}dinger-type formulation such as
Schr\"{o}dinger total energy, Schr\"{o}dinger potential and wave function are
also presented.
