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

On some one-dimensional quantum-mechanical models with a delta-potential interaction