  Scalar field cosmology is a model for dark energy and inflation. It has been
recently found that the standard Friedmann formulation of the scalar field
cosmology can be expressed in a non-linear Schr\"{o}dinger-type equation. The
new mathematical formulation is hence called non-linear Schr\"{o}dinger (NLS)
formulation which is suitable for a FRLW cosmological system with
non-negligible barotropic fluid density. Its major features are reviewed here.
