  We investigate four different types of representations of deformed canonical
variables leading to generalized versions of Heisenberg's uncertainty relations
resulting from noncommutative spacetime structures. We demonstrate explicitly
how the representations are related to each other and study three
characteristically different solvable models on these spaces, the harmonic
oscillator, the manifestly non-Hermitian Swanson model and an intrinsically
noncommutative model with Poeschl-Teller type potential. We provide an
analytical expression for the metric in terms of quantities specific to the
generic solution procedure and show that when it is appropriately implemented
expectation values are independent of the particular representation. A recently
proposed inequivalent representation resulting from Jordan twists is shown to
lead to unphysical models. We suggest an anti-PT-symmetric modification to
overcome this shortcoming.
