Simple applications of q-bosons

A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU(2) algebra is derived using the quantum analogue of th e anharmonic oscillator. We use the quantum oscillator algebra or q-boson a lgebra, which is a generalization of the Heisenberg-Weyl algebra obtained b y introducing a deformation parameter q. Further, we present a new algebrai c realization of the q-bosons, for the case of q being a root of unity, whi ch corresponds to a periodic structure described by a finite-dimensional re presentation. We show that this structure represents the symmetry of a line ar lattice with periodic boundary conditions.