  For a q-deformed harmonic oscillator, we find explicit coordinate
representations of the creation and annihilation operators, eigenfunctions, and
coherent states (the last being defined as eigenstates of the annihilation
operator). We calculate the product of the coordinate momentum uncertainties in
qoscillator eigenstates and in coherent states. For the oscillator, this
product is minimum in the ground state and equals 1/2, as in the standard
quantum mechanics. For coherent states, the $q$-deformation results in a
violation of the standard uncertainty relation; the product of the coordinate-
and momentumoperator uncertainties is always less than 1/2. States with the
minimum uncertainty, which tends to zero, correspond to the values of $\lambda$
near the convergence radius of the $q$-exponential.
