An analogue of the unitary displacement operator for the q-oscillator

Abstract

Using the concept of a non-standard Hilbert space over the quantum complex plane recently introduced by Kowalski et. al. (1993), we construct a unitary q-analogue of the Weyl-displacement operator. We investigate the q-displaced vacuum states and show that they exhibit properties analogous to coherent states in the undeformed theory. They are, however, distinct from any q-coherent states previously found in the literature.