Quantum mechanics on the noncommutative plane and sphere
By V. Nair, A. Polychronakos. 2000
352 citations recorded by the source corpus.
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 with the density of states becoming 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.
Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/df62fd039f58d96942a7bad77fa55d123e044b33
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In Applied Mathematics
In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- κ-Minkowski spacetime and the star product realizations (2007, methodology): “In the analyzis of κ-Minkowski spaces we use the methods developed for deformed single and multimode oscillators in the Fock space representations [34]-[40].”
- Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces (2003, background): “The significance of the points B = ± θ−1 has been previously noted within different field theoretic contexts in [30]–[33] and within the context of noncommutative quantum mechanics in [15, 16, 21].”
- The Non-commutative Landau Problem (2002, background): “(3.12) Explicitely, Souriau’s rule yields σE = d~p ∧ d~x+ θdp1 ∧ dp2 +Bdx1 ∧ dx2 − (~p · d~p+ dV ) ∧ dt, (3.13) whereas the Poisson bracket posited in the NC approach corresponds to the manifestly different two-form σNC = 1 m∗ [ d~p ∧ d~x+ θdp1 ∧ dp2 +Bdx1 ∧ dx2 ] − (~p · d~p + dV ) ∧ dt. (3.14)”
- New realizations of Lie algebra kappa-deformed Euclidean space (2006, methodology): “(left and right) ordering of NC coordinates [12, 18]. We analyze κ-deformed Euclidean space using the methods developed for deformed single and multimode oscillators in the Fock space representations [19, 20, 21, 22, 23, 24, 25, 26]. Particularly, we use the methods for constructing deformed creatio”