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We study some quantum systems described by noncanonical commutation relationsformally expressed as [q,p]=ihbar(I + chi H), where H is the associated(harmonic oscillator-like) Hamiltonian of the system, and chi is a Hermitian(constant) operator, i.e. [H,chi]=0 . In passing, we also consider a simple(chi=0 canonical) model, in the framework of a relativistic Klein-Gordon-likewave equation.

Supersymmetry, quark confinement and the harmonic oscillator