  We compare predictions from two familiar models of the metastable supercooled
liquid respectively constructed with thermodynamic and dynamic approach. In the
so called density functional theory (DFT) the free energy $F[\rho]$ of the
liquid is a functional of the inhomogeneous density $\rho({\bf r})$. The
metastable state is identified as a local minimum of $F[\rho]$. The sharp
density profile characterizing $\rho({\bf r})$ is identified as a single
particle oscillator, whose frequency is obtained from the parameters of the
optimum density function. On the other hand, a dynamic approach to supercooled
liquids is taken in the mode coupling theory (MCT) which predict a sharp
ergodicity-nonergodicity transition at a critical density. The single particle
dynamics in the non-ergodic state, treated approximately, represents a
propagating mode whose characteristic frequency is computed from the
corresponding memory function of the MCT. The mass localization parameters in
the above two models (treated in their simplest forms) are obtained
respectively in terms of the corresponding natural frequencies depicted and are
shown to have comparable magnitudes.
