Quantum mechanics on the noncommutative plane and sphere

Abstract

We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point, where the density of states becomes infinite, for the value of the magnetic field equal to the inverse of the noncommutativity parameter. The Landau problem on the noncommutative two-sphere is also solved and compared to the plane problem.

12 pages, no figures; references added

References in corpus (2)

• The exotic Galilei group and the "Peierls substitution"
• Monopoles and Strings in Noncommutative Gauge Theory

Cited by in corpus (279)

• Non-Commutative Quantum Mechanics
• Feynman Path Integral on the Noncommutative Plane
• Noncommutative Gravitational Quantum Well
• Noncommutative Quantum Mechanics from Noncommutative Quantum Field Theory
• Exotic galilean symmetry in the non-commutative plane, and the Hall effect
• Testing Non-commutative QED, Constructing Non-commutative MHD
• Duality in Scalar Field Theory on Noncommutative Phase Spaces
• UV divergence-free QFT on noncommutative plane
• Aharonov-Bohm Effect in Noncommutative Spaces
• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• Two phases of the noncommutative quantum mechanics
• The non-commutative Landau problem
• Fractional Angular Momentum in Noncommutative Space
• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
• On spherical harmonics for fuzzy spheres in diverse dimensions
• Hall Effect in Noncommutative Coordinates
• Testing spatial noncommutativiy via the Aharonov-Bohm effect
• Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
• Isotropic representation of noncommutative 2D harmonic oscillator
• Noncommutative Geometry and Cosmology
• Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
• Non-commutative Oscillators and the commutative limit
• Spectrum of Schroedinger field in a noncommutative magnetic monopole
• Testing Spatial Noncommutativity via Rydberg Atoms
• Covariant realizations of kappa-deformed space
• Topics in Noncommutative Geometry Inspired Physics
• Quantum Mechanics on the Noncommutative Torus
• Dual families of non-commutative quantum systems
• Scaling of variables and the relation between noncommutative parameters in Noncommutative Quantum Mechanics
• Noncommutativity in Field Space and Lorentz Invariance Violation
• The noncommutative harmonic oscillator in more than one dimensions
• A comparative review of four formulations of noncommutative quantum mechanics
• Non-relativistic anyons, exotic Galilean symmetry and noncommutative plane
• On noncommutative isotropic harmonic oscillator
• Aspects of Phase-Space Noncommutative Quantum Mechanics
• Seiberg-Witten map and Galilean symmetry violation in a non-commutative planar system
• Representation of noncommutative phase space
• Interactions and non-commutativity in quantum Hall systems
• Spectrum of the non-commutative spherical well
• Composite system in noncommutative space and the equivalence principle
• Phase-Space Noncommutativity and the Dirac Equation
• Quantum Theory of Noncommutative Fields
• Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics
• Berry Phase in the Gravitational Quantum Well and the Seiberg-Witten map
• (Super)Oscillator on CP(N) and Constant Magnetic Field
• Noncommutative 3D harmonic oscillator
• Remarks on the Noncommutative Gravitational Quantum Well
• Magnetic fields in noncommutative quantum mechanics
• Newton's Second Law in a Noncommutative Space
• Phases in noncommutative quantum mechanics on (pseudo)sphere
• Noncommutative Quantum Mechanics and Seiberg-Witten Map
• Quantum mechanics on noncommutative Riemann surfaces
• The Noncommutative Anandan's Quantum Phase
• Generalized kappa-deformed spaces, star-products, and their realizations
• Orbital Magnetism of Two-Dimension Noncommutative Confined System
• Noncommutative Dirac oscillator in an external magnetic field
• Representations of noncommutative quantum mechanics and symmetries
• Noncommutative oscillator, symmetry and Landau problem
• Magnetic-Dipole Spin Effects in Noncommutative Quantum Mechanics
• Time-Space Noncommutativity in Gravitational Quantum Well scenario
• Thermodynamical properties of graphene in noncommutative phase-space
• Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect
• Noncommutative Quantum Scattering in a Central Field
• Quantum Mechanics on Noncommutative Spacetime
• Probing phase-space noncommutativity through quantum beating, missing information and the thermodynamic limit
• Noncommutativity due to spin
• Noncommutative Graphene
• Noncommutative Quantum Mechanics and rotating frames
• Landau Problem in Noncommutative Quantum Mechanics
• Gauge Covariance of the Aharonov-Bohm Phase in Noncommutative Quantum Mechanics
• Landau Analog Levels for Dipoles in the Noncommutative Space and Phase Space
• Wigner Measures in Noncommutative Quantum Mechanics
• Spin and exotic Galilean symmetry
• Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space
• Exotic galilean symmetry and non-commutative mechanics
• Quantum mechanics on noncommutative plane and sphere from constrained systems
• Aharonov-Bohm effect in a Class of Noncommutative Theories
• Noncommutative Differential Forms on the kappa-deformed Space
• COW test of the weak equivalence principle: A low-energy window to look into the noncommutative structure of space-time?
• Anyons with anomalous gyromagnetic ratio & the Hall effect
• Tensor Operators in Noncommutative Quantum Mechanics
• Fundamental length in quantum theories with PT-symmetric Hamiltonians
• Newton equation for canonical, Lie-algebraic and quadratic deformation of classical space
• Quantum dissipation induced noncommutative geometry
• Exact solution of two dimensional Dunkl harmonic oscillator in Non-Commutative phase-space
• Quantum phase transitions in the noncommutative Dirac Oscillator
• A new approach to non-commutative inflation
• Space-Time Noncommutativity from Particle Mechanics
• On uncertainty relations in noncommutative quantum mechanics
• On Noncommutative Classical Mechanics
• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• Deformed Two-Photon Squeezed States in Noncommutative Space
• On the Landau system in noncommutative phase-space
• Violation of the Robertson-Schrödinger uncertainty principle and non-commutative quantum mechanics
• Lamb shift and Stark effect in simultaneous space-space and momentum-momentum noncommutative quantum mechanics and $\theta$-deformed $su(2)$ algebra
• Quantum Fields with Noncommutative Target Spaces
• A Deformation Quantization Theory for Non-Commutative Quantum Mechanics
• Noncommutative quantum mechanics and skew scattering in ferromagnetic metals
• Quantum field theory in generalised Snyder spaces
• The $\star$-value Equation and Wigner Distributions in Noncommutative Heisenberg algebras
• Dynamical symmetries in noncommutative theories
• The Wigner distribution function for the one-dimensional parabose oscillator
• Quantum Oscillator on $\DC P^n$ in a constant magnetic field
• The non-commutative and discrete spatial structure of a 3D Wigner quantum oscillator
• Jacobson generators, Fock representations and statistics of sl(n+1)
• Coherent States of the Deformed Heisenberg-Weyl Algebra in Noncommutative Space
• Effect of coordinate noncommutativity on the mass of a particle in a uniform field and the equivalence principle
• Supersymmetric Quantum Mechanics on Non-Commutative Plane
• Galilean symmetry in noncommutative field theory
• Dynamics of a Dirac Fermion in the presence of spin noncommutativity
• Asymptotic freedom for $\lambda {\varphi }_{\star }^4$ QFT in Snyder-de Sitter space
• Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane
• Noncommutative quantum mechanics and Bohm's ontological interpretation
• Exact master equation for a noncommutative Brownian particle
• Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action
• Noncommutative Space Corrections on the Klein-Gordon and Dirac Oscillators Spectra
• Classical Mechanics on Noncommutative Space with Lie-algebraic Structure
• Non-singular Brans-Dicke collapse in deformed phase space
• Emergence of Geometric phase shift in Planar Non-commutative Quantum Mechanics
• Landau Levels in the noncommutative $Ad{S}_2$
• Thermodynamics of Quantum Phase Transitions of a Dirac oscillator in a homogenous magnetic field
• Non-Hermitian quantum mechanics in non-commutative space
• Supersymmetric quantum mechanics on noncommutative space
• Noncommutative relativistic particles
• U(1) gauge invariant noncommutative Schrödinger theory and gravity
• Chiral Bosons in Noncommutative Spacetime
• Non-commutative oscillator with Kepler-type dynamical symmetry
• Noncommutative Field Theory from Quantum Mechanical Space-Space Noncommutativity
• Non-commutative Supersymmetric Quantum Mechanics
• A Simple Signal of Noncommutative Space
• Noncommutative configuration space. Classical and quantum mechanical aspects
• Angular momentum quantum backflow in the noncommutative plane
• Finite Number of States, de Sitter Space and Quantum Groups at Roots of Unity
• Nonlinear Holomorphic Supersymmetry on Riemann Surfaces
• Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems
• Response of simple quantum systems to different polarizations of gravitational waves in noncommutative phase-space
• Snyder-type spaces, twisted Poincaré algebra and addition of momenta
• Constant magnetic field and 2d non-commutative inverted oscillator
• Noncommutativity and Reparametrisation symmetry
• Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential
• Exotic plasma as classical Hall Liquid
• Tensor Coordinates in Noncommutative Mechanics
• Dynamical noncommutativity
• Resonant-bar detectors of gravitational wave as possible probe of the noncommutative structure of space
• Galilean symmetry in noncommutative Gravitational Quantum Well
• Noncommutative Geometry and Fluid Dynamics
• Noncommutative Geometry and Geometric Phases
• Fractional quantum Hall effect on the two-sphere: a matrix model proposal
• Free-fall in a uniform gravitational field in non-commutative quantum mechanics
• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Noncommutativity in (2+1)-dimensions and the Lorentz group
• Un-equivalency Theorem between Deformed and undeformed Heisenberg-Weyl's Algebras
• A new approach to the analysis of a noncommutative Chern-Simons theory
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Footprint of spatial noncommutativity in resonant detectors of gravitational wave
• Chiral bosonization for non-commutative fields
• Lowest Landau level theory of the bosonic Jain states
• Noncommutative field gas driven inflation
• Berry's phase in noncommutative spaces
• Equations of motion, Noncommutativity and Quantization
• Associative realizations of $\kappa$-deformed extended Snyder model
• Matrix oscillator and Calogero-type models
• Non-commuting coordinates, exotic particles, & anomalous anyons in the Hall effect
• Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation
• Holographic duals to Poisson sigma models and noncommutative quantum mechanics
• Noncommutativity from Embedding Techniques
• Spin Non-commutativity and the Three-Dimensional Harmonic Oscillator
• Searching for Effects of Spatial Noncommutativity via Chern-Simons' Processes
• Test of Quantum Effects of Spatial Noncommutativity using Modified Electron Momentum Spectroscopy
• Entangled state representations in noncommutative quantum mechanics
• A path integral leading to higher-order Lagrangians
• Representations of the Lie Superalgebra gl(1|n) in a Gel'fand-Zetlin Basis and Wigner Quantum Oscillators
• Thermodynamics of a charged particle in a noncommutative plane in a background magnetic field
• The Noncommutative Doplicher-Fredenhagen-Roberts-Amorim Space
• Commutator Anomaly in Noncommutative Quantum Mechanics
• Noncommutative Coulombic Monopole
• Dimensional Reduction via Noncommutative Spacetime: Bootstrap and Holography
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Wong's Equations and Charged Relativistic Particles in Non-Commutative Space
• Non-Commutative Geometry and Measurements of Polarized Two Photon Coincidence Counts
• Induced entanglement entropy of harmonic oscillators in noncommutative phase space
• 1-D Harmonic Oscillator in Snyder Space, the Classic and the Quantum
• Exploring the thermodynamics of non-commutative scalar fields
• Signatures of noncommutativity in bar detectors of gravitational waves
• Two-particle system in noncommutative space with preserved rotational symmetry
• Magnetic Seed and Cosmology as Quantum Hall Effect
• Fingerprints of the quantum space-time in time-dependent quantum mechanics: An emergent geometric phase
• Exact solution of damped harmonic oscillator with a magnetic field in a time dependent noncommutative space
• Non-Commutative Corrections to the MIC-Kepler Hamiltonian
• On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
• Remarks on the Formulation of Quantum Mechanics on Noncommutative Phase Spaces
• Equivalence principle in context of large uniform acceleration - a quantum mechanical perspective
• Noncommutative Supersymmetry in Two Dimensions
• Physical Observables for Noncommutative Landau Levels
• From Feynman Proof of Maxwell Equations to Noncommutative Quantum Mechanics
• A Variational Formulation of Symplectic Noncommutative Mechanics
• Canonical, Lie-algebraic and quadratic twist deformations of Galilei group
• Extended Space Duality in the Noncommutative Plane
• Analytical and numerical analysis of a rotational invariant D=2 harmonic oscillator in the light of different noncommutative phase-space configurations
• Pauli equation on noncommutative plane and the Seiberg-Witten map
• Bound state energies and phase shifts of a non-commutative well
• Generalized relativistic kinematics in Poincaré-invariant models
• Aspects of Quantum Gravity in Cosmology
• A complete solution of a Constrained System: SUSY Monopole Quantum Mechanics
• Noncommutative quantum mechanics of simple matter systems interacting with circularly polarized gravitational waves
• Landau levels in a 2D noncommutative space: matrix and quaternionic vector coherent states
• Structure of Noncommutative Fock space
• Phase space quantization, noncommutativity and the gravitational field
• Gauge invariant energy spectra in 2-dimensional noncommutative quantum mechanics
• Deformed Two-Mode Quadrature Operators in Noncommutative Space
• Lagrangian versus Quantization
• Gravitational Quantum Well
• Path integral action of a particle in a magnetic field in the noncommutative plane and the Aharonov-Bohm effect
• Path integral action and Chern-Simons quantum mechanics in noncommutative plane
• Noncommutative Complex Scalar Field and Casimir Effect
• Quantum Theory of Tensionless Noncommutative p-Branes
• On the Quantization of Length in Noncommutative Spaces
• Heisenberg Evolution in a Quantum Theory of Noncommutative Fields
• Symplectic Deformations, Non Commutative Scalar Fields and Fractional Quantum Hall Effect
• Deformed "Commutative" Chern - Simons System
• Voros product and the Pauli principle at low energies
• Weak-strong duality of the non-commutative Landau problem induced by a two-vortex permutation, and conformal bridge transformation
• The quantum and Klein-Gordon oscillators in a non-commutative complex space and the thermodynamic functions
• Localization at threshold in noncommutative space
• Loop Quantum Cosmology with a noncommutative quantum deformed photon gas
• Noncommutative Lagrange Mechanics
• Trace of phase-space noncommutativity in the response of a free particle to linearized gravitational waves
• Lagrangian and Noncommutativity
• Constrained Dynamics of an Anomalous $(g/neq2)$ Relativistic Spinning Particle in Electromagnetic Background
• Gauge invariance and classical dynamics of noncommutative particle theory
• Testing Spatial Noncommutativity via Magnetic Hyperfine Structure Induced by Fractional Angular Momentum of Rydberg System
• Particle-antiparticle asymmetry from magnetogenesis through the Landau mechanism
• Collapsing Shells and Black Holes: a quantum analysis
• Quantum Error Correction in the Lowest Landau Level
• Dark Matter in a bi-metric universe
• On the noncommutative eikonal
• Quantum dot with spin-orbit interaction in noncommutative phase space and analog Landau levels
• Twisted Supersymmetry in a Deformed Wess-Zumino Model in (2+1) Dimensions
• Weighted Lorentz invariant measures as quantum field theory regulators
• Uncertainty relations for a non-canonical phase-space noncommutative algebra
• Galilei Group with multiple central extension, vorticity and entropy generation: "Exotic" fluid in 3+1-dimensions
• Quantum simulation of quantum mechanical system with spatial noncommutativity
• Cohomological Operators and Covariant Quantum Superalgebras
• Lyapunov exponents and entanglement entropy transition on the noncommutative hyperbolic plane
• Remarks on the representation theory of the Moyal plane
• Modified Lorentz transformations in deformed special relativity
• Path-integral action of a particle in the noncommutative phase-space
• Two-dimensional Noncommutative atom Gas with Anandan interaction
• Lie algebraic noncommuting structures from reparametrisation symmetry
• Connes spectral distance and nonlocality of generalized noncommutative phase spaces
• Waves on Noncommutative Spacetimes
• Noncommutative real scalar field theory in 2+1 dimensions at finite temperature
• Supersymmetry breaking in noncommutative quantum mechanics
• Algebraic Structure of Dirac Hamiltonians in Non-Commutative Phase Space
• Dynamics determines geometry
• Exotic galilean symmetry and the Hall effect
• Inverse square problem and so(2,1) symmetry in noncommutative space
• Nonlocal, noncommutative picture in quantum mechanics and distinguished canonical maps
• Integrable generalisations of Dirac magnetic monopole
• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• Perturbed nonlinear models from Noncommutativity
• Zitterbewegung in Noncommutative Geometry
• A Family of Non-commutative geometries
• Noncommutative scalar fields from symplectic deformation
• Accessing the non-equal-time commutators of a trapped ion
• Exotic Newton-Hooke group, noncommutative plane and superconformal symmetry
• Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism
• Lattice oscillator model on noncommutative space: eigenvalues problem for the perturbation theory
• Theories on noncommutative spaces and deformed symmetries
• Uncertainty Relations for the Relativistic Jackiw-Nair Anyon: A First Principles Derivation
• Dimensional Reduction for Generalized Poisson Brackets
• Cryptohermitian Hamiltonians on graphs. II. Hermitizations
• Heisenberg quantization for the systems of identical particles and the Pauli exclusion principle in noncommutative spaces
• Quantization of Length in Spaces with Position-Dependent Noncommutativity
• Electromagnetic Excitations of Hall Systems on Four Dimensional Space
• Spectra of disc operator for twisted acceleration-enlarged Newton-Hooke space-times
• Statistical interparticle potential on noncommutative space
• Dynamic and static properties of Quantum Hall and Harmonic Oscillator systems on the non-commutative plane