The vector DKP oscillator in the plane within the context of the extended uncertainty principle

Abstract

The Extended Uncertainty Principle (EUP) is a gravitational correction to quantum mechanics that extends and modifies Heisenberg’s uncertainty principle. Particularly, it suggests the existence of a minimum measurable momentum scale, often referred to as the Minimal Momentum (MM), a quantity which is expected to influence the properties of all quantum mechanical systems. In this paper we investigate the effects of the EUP on the quantum features of the Two-Dimensional (2D) Duffin-Kemmer-Petiau Oscillator (DKPO) for spin-one particles subject to an external Homogeneous Magnetic Field (HMF). Using the position representation, we solve the corresponding problem and we obtain the exact wave functions and eigenenergies of the system, then we analyze how they are affected by the MM. We also examine the special case of a spin-one particle moving in a plane under a perpendicular HMF.

Keywords

• DKP oscillator
• Quantum theory
• Extended uncertainty principle
• Theoretical study