A single trapped ion in a finite range trap

► We present a method to describe dynamics of an ion confined in a finite size trap. ► The trap is modeled with a potential in the context of an f-deformed oscillator. ► The ion exhibits nonclassical properties such as squeezing and quantum interference. ► Also this system can be used to generate highly excited motional Fock state. ► The Hilbert space size effects and nano traps can be investigated by this model.