COHERENT STATES OF THE Q-WEYL ALGEBRA

New coherent states of the q-Weyl algebra AA(+) - qA(+)A = 1,0 < q < 1 , are constructed. They are defined as eigenstates of the operator At which is the lowering operator for nonhighest weight representations d escribing positive energy states. Depending on whether the positive sp ectrum is discrete or continuous, these coherent states are related ei ther to the bilateral basic hypergeometric series or to some integrals over them. The free particle realization of the q-Weyl algebra when A (+)A proportional to d(2)/dx(2) is used for illustrations.