In the weak deformation (WD) approximation of the WeylHeisenberg algebra, the corresponding generalized coherent states and displacement operator are constructed. It is shown that those states, and contrary to the non-deformed Weyl-Heisenberg algebra, are not eigenstates of the annihilation operator. Moreover, and as an alternative to the Chaïchian et al. Q-deformed path integral approach (where Q is the deformation parameter), using the Bargmann Fock representation, we propose in the WD approximation, a general simple formalism. As an application, we calculate the propagator and the wave function of the harmonic oscillator.PACS Nos.: 03.65.Fd, 31.15.Kb
This paper has been motivated by a recent paper by Dey [Phys. Rev. D 91, 044024 (2015)] on the known Arik-Coon
q oscillator. We construct
q coherent, even and odd
q-cat states in Fock representation for the Biedenharn-Macfarlane
q oscillator with
q>1 and study their nonclassical properties. The
q-coherent states minimize the Heisenberg uncertainty relation between the generalized position and momentum operators as well as the
x and
y components of a
q-deformed
su(1,1) algebra in the Schwinger boson representation. The latter is also minimized by the even and odd
q-cat states. We show that, contrary to the undeformed harmonic oscillator, the squeezing effect in both position and momentum operators can be exhibited by odd
q-cat states. It is also violated by even
q-cat states. Furthermore, it is shown that the antibunching effect and sub-Poissonian or super-Poissonian statistics can simultaneously appear by each of the even or odd
q-cat states. Finally, a unitary Fock representation of the
q-deformed
su(1,1) algebra is obtained by the
q-deformed Bargmann-Fock realization.