The symmetric Tamm–Dancoff q-oscillator: the representation, quasi-Fibonacci nature, accidental degeneracy and coherent states

Abstract

In this paper we propose a symmetric q-deformed Tamm–Dancoff (S-TD) oscillator algebra and study its representation, coordinate realization, and main properties. In particular, the non-Fibonacci (more exactly, quasi-Fibonacci) nature of the S-TD oscillator is established, the possibility of relating it to a certain -deformed oscillator family is shown, and the occurrence of pairwise accidental degeneracy is proven. We also find the coherent state for the S-TD oscillator and show that it satisfies a completeness relation. The main advantage of the S-TD model over the usual Tamm–Dancoff oscillator is that due to the symmetry, it admits not only real, but also complex (phase-like) values of the deformation parameter q.