Energy corrections due to the noncommutative phase-space of the charged isotropic harmonic oscillator in a uniform magnetic field in 3D
arXiv:2105.08516 · doi:10.1088/1402-4896/abf9d4
Abstract
In this study, we investigate the effects of noncommutative Quantum Mechanics in three dimensions on the energy levels of a charged isotropic harmonic oscillator in the presence of a uniform magnetic field in the z-direction. The extension of this problem to three dimensions proves to be non-trivial. We obtain the first-order corrections to the energy-levels in closed form in the low energy limit of weak noncommutativity. The most important result we can note is that all energy corrections due to noncommutativity are negative and their magnitude increase with increasing Quantum numbers and magnetic field.
arXiv comment13 pages, 3 figues. arXiv admin note: text overlap with arXiv:2008.04076
References in corpus (41)
- Large N Field Theories, String Theory and Gravity
- String Theory and Noncommutative Geometry
- Hilbert Space Representation of the Minimal Length Uncertainty Relation
- Quantum Field Theory on Noncommutative Spaces
- The quantum structure of spacetime at the Planck scale and quantum fields
- Noncommutative Geometry and Matrix Theory: Compactification on Tori
- Non-Commutative Quantum Mechanics
- Magnetic fields, branes and noncommutative geometry
- Features of Time-independent Wigner Functions
- String theories with deformed energy momentum relations, and a possible non-tachyonic bosonic string
- The Landau problem and noncommutative quantum mechanics
- The non-commutative Landau problem
- Hall Effect in Noncommutative Coordinates
- A Novel Approach to Noncommutativity in Planar Quantum Mechanics
- Interactions and non-commutativity in quantum Hall systems
- Theory of exciton fine structure in semiconductor quantum dots: quantum dot anisotropy and lateral electric field
- Noncommutative Superspace, Supermatrix and Lowest Landau Level
- A new look at loop quantum gravity
- Wigner Functions for the Landau Problem in Noncommutative Spaces
- Spin-spin coupling in electrostatically coupled quantum dots
- Noncommutative oscillator, symmetry and Landau problem
- Planck scale Corrections to the Harmonic Oscillator, Coherent and Squeezed States
- PT-symmetric noncommutative spaces with minimal volume uncertainty relations
- Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect
- Landau Problem in Noncommutative Quantum Mechanics
- Energy-dependent noncommutative quantum mechanics
- Landau Analog Levels for Dipoles in the Noncommutative Space and Phase Space
- Simple model for quantum general relativity from loop quantum gravity
- Probing noncommutative theories with quantum optical experiments
- Quantum Hall Effect In Bilayer Systems And The Noncommutative Plane: A Toy Model Approach
- On the Landau system in noncommutative phase-space
- Generalized Uncertainty Principle Corrections to the Simple Harmonic Oscillator in Phase Space
- Super-extended noncommutative Landau problem and conformal symmetry
- Landau Levels in the noncommutative
- Spectral Regularisation: Induced Gravity and the Onset of Inflation
- Orbital effects of a strong in-plane magnetic field on a gate-defined quantum dot
- Twist Deformation of Rotationally Invariant Quantum Mechanics
- Correlation energy of anisotropic quantum dots
- Effects of Twisted Noncommutativity in Multi-particle Hamiltonians
- Physical Observables for Noncommutative Landau Levels
- Bohr-van Leeuwen theorem in non-commutative space