Supersymmetry, quark confinement and the harmonic oscillator

We study some quantum systems described by noncanonical commutation relations formally 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-like wave equation.Comment: To be published in Journal of Physics A: Mathematical and Theoretical (2007