Exact solutions of the (2+1) Dimensional Dirac equation in a constant magnetic field in the presence of a minimal length

Abstract

We study the (2+1) dimensional Dirac equation in an homogeneous magnetic field (relativistic Landau problem) within a minimal length, or generalized uncertainty principle -GUP-, scenario. We derive exact solutions for a given explicit representation of the GUP and provide expressions of the wave functions in the momentum representation. We find that in the minimal length case the degeneracy of the states is modified and that there are states that do not exist in the ordinary quantum mechanics limit (β-->0). We also discuss the mass-less case which may find application in describing the behavior of charged fermions in new materials like Graphene.

9 pages, to appear in Physical Review D

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Cited by in corpus (33)

• GUP Modified Hawking Radiation in Bumblebee Gravity
• Entangled Particles Tunneling From a Schwarzschild Black Hole immersed in an Electromagnetic Universe with GUP
• Singular inverse square potential in coordinate space with a minimal length
• Kratzer's molecular potential in quantum mechanics with a generalized uncertainty principle
• On the (2+1)-dimensional Dirac equation in a constant magnetic field with a minimal length uncertainty
• Quantum phase transitions of the Dirac oscillator in a minimal length scenario
• Exact solutions of the (2+1) -dimensional Dirac oscillator under a magnetic field in the presence of a minimal length in the noncommutative phase-space
• Thermal properties of a two-dimensional Duffin-Kemmer-Petiau oscillator under an external magnetic field in the presence of a minimal length
• Generalized relativistic harmonic oscillator in minimal length quantum mechanics
• Pseudoharmonic oscillator in quantum mechanics with a minimal length
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• Dirac $\delta$-function potential in quasiposition representation of a minimal-length scenario
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• Particle in a cavity in one-dimensional bandlimited quantum mechanics
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