  We discuss a systematic construction of dimensionless quantum-mechanical
equations. The process reduces the number of independent model parameters to a
minimum and, at the same time, provides the natural units of length, energy,
etc. in a clear, straightforward way. We compare this systematic procedure with
the widely adopted one that consists of setting $\hbar=1$. As illustrative
examples, we choose some simple one-dimensional models proposed recently for
the study of localized states in inhomogeneous media.
