Even and odd q-coherent state representations of the quantum Heisenberg-Weyl algebra

Abstract

Even and odd q-coherent states are introduced in terms of the q-functions defined in the paper. It is shown that the even and odd q-coherent states form a new kind of representation of the quantum Heisenberg-Weyl algebra which is realized in the form of matrix q-differential operators in the even and odd q-coherent state space.