Symmetric Tamm-Dancoff q-oscillator: 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 S-TD oscillator is established, the possibility of relating it to certain p,q-deformed oscillator family shown, the occurrence of the pairwise accidental degeneracy proven. We also find the coherent state for the S-TD oscillator and show that it satisfies completeness relation. Main advantage of the S-TD model over usual Tamm-Dancoff oscillator is that due to (q<-->q^{-1})- symmetry it admits not only real, but also complex (phase-like) values of the deformation parameter q.

14 pages; v2: minor revision, references and paragraph in Conclusions added, accepted for publication in J.Phys.A

References in corpus (3)

• Deformed gas of p,q-bosons: virial expansion and virial coefficients
• Interacting particles system revisited in the framework of the q-deformed algebra
• A q-Oscillator with 'Accidental' Degeneracy of Energy Levels