  We introduce a generalization of the Jaynes-Cummings model and study some of
its properties. We obtain the energy spectrum and eigenfunctions of this model
by using the tilting transformation and the squeezed number states of the
one-dimensional har- monic oscillator. As physical applications, we connect
this new model to two important and novelty problems: the relativistic
parametric amplifier and the quantum simulation of a single trapped ion.
