AN ANALOG OF THE UNITARY DISPLACEMENT OPERATOR FOR THE Q-OSCILLATOR

Using the concept of a non-standard Hilbert space over the quantum complex plane recently introduced by Kowalski et al [1], 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.