On uncertainty relations in noncommutative quantum mechanics
arXiv:hep-th/0208162 · doi:10.1016/S0370-2693(02)02731-4
Abstract
We discuss the uncertainty relations in quantum mechanics on noncommutative plane. In particular, we show that, for a given state at most one out of three basic nontrivial uncertainty relations can be saturated. We consider also in some detail the case of angular momentum eigenstates.
8 pages, revised version, few references added
References in corpus (21)
- String Theory and Noncommutative Geometry
- Noncommutative Geometry and Matrix Theory: Compactification on Tori
- Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED
- Noncommutative Open String and D-brane
- D-branes and Deformation Quantization
- Non-Commutative Quantum Mechanics
- Quantum mechanics on the noncommutative plane and sphere
- Magnetic fields, branes and noncommutative geometry
- The exotic Galilei group and the "Peierls substitution"
- Constrained Quantization of Open String in Background B Field and Noncommutative D-brane
- Galilean-Invariant (2+1)-Dimensional Models with a Chern-Simons-Like Term and D=2 N oncommutative Geometry
- The Landau problem and noncommutative quantum mechanics
- Non-commutative Oscillators and the commutative limit
- Spectrum of Schroedinger field in a noncommutative magnetic monopole
- Quantum Mechanics on the Noncommutative Torus
- A Novel Approach to Noncommutativity in Planar Quantum Mechanics
- Non-relativistic anyons, exotic Galilean symmetry and noncommutative plane
- Quantum Mechanics on a Noncommutative Brane in M(atrix) Theory
- Quantum mechanics on noncommutative plane and sphere from constrained systems
- Holomorphic Quantization on the Torus and Finite Quantum Mechanics
- Negative Probability and Uncertainty Relations
Cited by in corpus (19)
- Composite system in noncommutative space and the equivalence principle
- Poincare covariant mechanics on noncommutative space
- Representations of noncommutative quantum mechanics and symmetries
- Entropic Gravity, Phase-Space Noncommutativity and the Equivalence Principle
- Probing phase-space noncommutativity through quantum beating, missing information and the thermodynamic limit
- A Deformation Quantization Theory for Non-Commutative Quantum Mechanics
- Coherent States of the Deformed Heisenberg-Weyl Algebra in Noncommutative Space
- Exact master equation for a noncommutative Brownian particle
- U(1) gauge invariant noncommutative Schrödinger theory and gravity
- Commutator Anomaly in Noncommutative Quantum Mechanics
- N=2 supersymmetric Pais-Uhlenbeck oscillator
- Structure of Noncommutative Fock space
- Quantum Theory of Tensionless Noncommutative p-Branes
- On the Quantization of Length in Noncommutative Spaces
- Quantum mechanics on non commutative spaces and squeezed states: a functional approach
- Uncertainty relations for a non-canonical phase-space noncommutative algebra
- Time dependent transitions with time-space noncommutativity & its implications in Quantum Optics
- Zen and the Art of Space-Time Manufacturing
- Quantization of Length in Spaces with Position-Dependent Noncommutativity