Power-law expansion cosmology in Schrödinger-type formulation

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We investigate non-linear Schrödinger-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 Schrödinger wave function in this formulation is generally non-normalizable. Assuming power-law expansion, a tq, we obtain scalar field potential as function of time. The corresponding quantities in Schrödinger-type formulation such as Schrödinger total energy, Schrödinger potential and wave function are also presented.