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We study the classical and quantum oscillator in the context of anon-additive (deformed) displacement operator, associated with aposition-dependent effective mass, by means of the supersymmetric formalism.From the supersymmetric partner Hamiltonians and the shape invariance techniquewe obtain the eigenstates and the eigenvalues along with the ladders operators,thus showing a preservation of the supersymmetric structure in terms of thedeformed counterpartners. The deformed space in supersymmetry allows tocharacterize position-dependent effective mass, uniform field interactions andto obtain a generalized uncertainty relation (GUP) that behaves as adistinguishability measure for the coherent states, these latter satisfying aperiodic evolution of the GUP corrections.

Supersymmetric quantum mechanics and coherent states for a deformed oscillator with position-dependent effective mass