A comparative review of four formulations of noncommutative quantum mechanics

DOI10.1142/S0217751X16300258zbMath1344.81005arXiv1603.07176MaRDI QIDQ2820148

Laure Gouba

Publication date: 14 September 2016

Published in: International Journal of Modern Physics A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.07176

zbMATH Keywords

noncommutative geometrySeiberg-Witten mapstar productformalismpath-integralnoncommutative quantum mechanicsWeyl-Wigner transformBopp's shift

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Path integrals in quantum mechanics (81S40) Research exposition (monographs, survey articles) pertaining to quantum theory (81-02) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Noncommutative geometry in quantum theory (81R60) Deformation quantization, star products (53D55)

Related Items (15)

Unnamed Item ⋮ Classical limit and Ehrenfest's theorem versus non-relativistic limit of noncommutative Dirac equation in the presence of minimal uncertainty in momentum ⋮ Solutions of noncommutative two-dimensional position-dependent mass Dirac equation in the presence of Rashba spin-orbit interaction by using the Nikiforov-Uvarov method ⋮ Energy-dependent harmonic oscillator in noncommutative space: A path integral approach ⋮ Nonclassicality versus entanglement in a noncommutative space ⋮ Noncommutative Dirac and Schrödinger equations in the background of the new generalized Morse potential and a class of Yukawa potential with the improved Coulomb-like tensor potential as a tensor in 3D-ERQM and 3D-ENRQM symmetries ⋮ Heavy quarkonium systems for the deformed unequal scalar and vector Coulomb–Hulthén potential within the deformed effective mass Klein–Gordon equation using the improved approximation of the centrifugal term and Bopp’s shift method in RNCQM symmetries ⋮ Gravitational radiation in dynamical noncommutative spaces ⋮ Approximate \(k\)-state solutions of the deformed Dirac equation in spatially dependent mass for the improved Eckart potential including the improved Yukawa tensor interaction in ERQM symmetries ⋮ Gauge invariant energy spectra in 2-dimensional noncommutative quantum mechanics ⋮ A Squeezed Review on Coherent States and Nonclassicality for Non-Hermitian Systems with Minimal Length ⋮ Heat flow and noncommutative quantum mechanics in phase-space ⋮ Quantum, noncommutative and MOND corrections to the entropic law of gravitation ⋮ Pair creation of neutral Dirac particle in (1 + 2)d noncommutative spacetime ⋮ Entanglement in phase-space distribution for an anisotropic harmonic oscillator in noncommutative space

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