Quantum mechanics on the noncommutative plane and sphere

Preprint

9 January 2001

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.hep-th/0011172

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.

Keywords

PARTICLE IN A MAGNETIC
NONCOMMUTATIVE PLANE
DENSITY OF STATES
QUANTUM MECHANICS
CHARGED PARTICLE
LANDAU PROBLEM
MAGNETIC FIELD
CRITICAL POINT

All Related Versions

Version 1, 2000-11-19, ArXiv
Version 2, 2001-01-09, ArXiv
Published version: Physics Letters B, 505 (1-4), 267.

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