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We investigate four different types of representations of deformed canonicalvariables leading to generalized versions of Heisenberg's uncertainty relationsresulting from noncommutative spacetime structures. We demonstrate explicitlyhow the representations are related to each other and study threecharacteristically different solvable models on these spaces, the harmonicoscillator, the manifestly non-Hermitian Swanson model and an intrinsicallynoncommutative model with Poeschl-Teller type potential. We provide ananalytical expression for the metric in terms of quantities specific to thegeneric solution procedure and show that when it is appropriately implementedexpectation values are independent of the particular representation. A recentlyproposed inequivalent representation resulting from Jordan twists is shown tolead to unphysical models. We suggest an anti-PT-symmetric modification toovercome this shortcoming.

Hermitian versus non-Hermitian representations for minimal length uncertainty relations