  In this work we explore a generalization of the Dirac and Klein-Gordon (KG)
oscillators, provided with a deformed linear momentum inspired in nonextensive
statistics, that gives place to the Morse potential in relativistic contexts by
first principles. In the (1+1)-dimensional case the relativistic oscillators
are mapped into the quantum Morse potential. Using the Pekeris approximation,
in the (3+1)-dimensional case we study the thermodynamics of the S-waves states
(l=0) of the H2, LiH, HCl and CO molecules (in the non-relativistic limit) and
of a relativistic electron, where Schottky anomalies (due to the finiteness of
the Morse spectrum) and spin contributions to the heat capacity are reported.
By revisiting a generalized Pekeris approximation, we provide a mapping from
(3+1)-dimensional Dirac and KG equations with a spherical potential to an
associated one-dimensional Schr\"odinger-like equation, and we obtain the
family of potentials for which this mapping corresponds to a Schr\"odinger
equation with non-minimal coupling.
