2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210936We 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, $a \sim t^q$, 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.9 pages, 5 figures, Revtex 4, accepted by Astroparticle Physics, more Ref. addedGeneral Relativity and Quantum CosmologyAstrophysicsHigh Energy Physics - TheoryQuantum Physicstext