  A wide class of q-deformed harmonic oscillators including those of Macfarlane
type and of Dubna type is shown to be describable in a unified way. The
Hamiltonian of the oscillator is assumed to be given by a q-deformed
anti-commutator of the q-deformed ladder operators. By solving $q$-difference
equations, explicit coordinate representations of ladder operators and wave
functions are derived, and unified parametric representations are found for
$q$-Hermite functions and related formulas for the oscillators of Macfarlane
and Dubna types. In addition to the well-known solutions with globally periodic
structure, there exist an infinite number of solutions with globally aperiodic
structure.
