The Generalized Uncertainty Principle and the Semi-relativistic Harmonic Oscillator

We study the Massless Semi-Relativistic Harmonic Oscillator within the framework of quantum mechanics with a Generalized Uncertainty Principle (GUP). The latter derives from the idea of minimal observable length, a quantity whose existence is expected to affect the energy eigenvalues and the eigenfunctions of the system. These effects are worked out, to the first order in the deformation parameter, using a perturbative approach based on Brau’s representation of position and momentum operators. Besides, we have discussed the impact of the GUP on the known duality between the considered model and the Schrödinger equation with a linear potential.