Harmonic oscillator in the context of the extended uncertainty principle

Abstract

At large-scale distances where the space-time is curved due to gravity, a nonzero minimal uncertainty in the momentum, [Formula: see text], is being estimated to emerge. The presence of minimal uncertainty in momentum allows a modification to the quantum uncertainty principle, which is known as the extended uncertainty principle (EUP). In this work, we handle the harmonic oscillator problem in the EUP scenario and obtain analytical exact solutions in classical and semi-classical domains. In the classical context, we establish the equations of motion of the oscillator and show that the EUP-corrected frequency is depending on the energy and deformation parameter. In the semi-classical domain, we derive the energy eigenvalue levels and demonstrate that the energy spectrum depends on [Formula: see text], as the feature of hard confinement. Finally, we investigate the impact of the EUP on the harmonic oscillator’s thermodynamic properties by using the EUP-corrected partition functions in the classical limit in the (A)dS backgrounds.