  We show that a direct connection can be drawn, based on fundamental quantum
principles, between the Morse potential, extensively used as an empirical
description for the atomic interaction in diatomic molecules, and the harmonic
potential. This is conceptually achieved here through a non-additive
translation operator, whose action leads to a perfect equivalence between the
quantum harmonic oscillator in deformed space and the quantum Morse oscillator
in regular space. In this way, our theoretical approach provides a distinctive
first principle rationale for anharmonicity, therefore revealing a possible
quantum origin for several related properties as, for example, the dissociation
energy of diatomic molecules and the deformation of cubic metals.
