Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-th/0508060 · Modern Physics Letters A

COMMUTATOR ANOMALY IN NONCOMMUTATIVE QUANTUM MECHANICS

SAYIPJAMAL DULAT, KANG LI

Published Dec 21, 2006• 10 citations
arXivHTMLPDF

Abstract

In this paper, the Schrödinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space–space and space–momentum as well as momentum–momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.

DOI
10.1142/s0217732306020585

Related papers

Commutator Anomaly in Noncommutative Quantum Mechanics

Sayipjamal Dulat A, Kang Li B

In this letter, firstly, the Schr$\\ddot{o}$dinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space-space and space-momentum as well as momentum-momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.

•Jan 1, 2005•9 citations

REPRESENTATION OF NONCOMMUTATIVE PHASE SPACE

KANG LI, JIANHUA WANG, CHIYI CHEN

The representations of the algebra of coordinates and momenta of noncommutative phase space are given. We study, as an example, the harmonic oscillator in noncommutative space of any dimension. Finally the map of Schrödinger equation from noncommutative space to commutative space is obtained.

arXiv:hep-th/0409234•Modern Physics Letters A•Aug 24, 2005•73 citations

SCALING OF VARIABLES AND THE RELATION BETWEEN NONCOMMUTATIVE PARAMETERS IN NONCOMMUTATIVE QUANTUM MECHANICS

O. BERTOLAMI, J. G. ROSA, C. M. L. DE ARAGÃO +2 more

We consider noncommutative quantum mechanics with phase space noncommutativity. In particular, we show that a scaling of variables leaves the noncommutative algebra invariant, so that only the self-consistent effective parameters of the model are physically relevant. We also discuss the recently proposed relation of direct proportionality between the noncommutative parameters, showing that it has a limited applicability.

arXiv:hep-th/0509207•Modern Physics Letters A•Mar 28, 2006•93 citations

PATH INTEGRAL APPROACH TO NONCOMMUTATIVE QUANTUM MECHANICS

Branko G Dragovich, Zoran Rakić

We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the another one with usual commutative coordinates and momenta. We found connection between quadratic classical Hamiltonians, as well as Lagrangians, in their commutative and noncommutative regimes. The general procedure to compute Feynman's path integral on this noncommutative phase space with quadratic Lagrangians (Hamiltonians) is presented. Using this approach, a particle in a constant field, ordinary and inverted harmonic oscillators are elaborated in detail.

arXiv:hep-th/0401198•International Workshop on Lie Theory and Its Applications in Physics (LT)•Jul 1, 2004•12 citations

Minimalisation of uncertainty relations in noncommutative quantum mechanics

Piotr Kosiński, Katarzyna Bolonek-Lasoń

The explicit constrtuction of states saturating uncertainty relations following from basic commutation rules of NCQM is given both in Fock space and coordinate representation

arXiv:hep-th/0208213•Aug 29, 2002•3 citations

On uncertainty relations in noncommutative phase space

Guangjie Guo, Chaoyun Long, Shuijie Qin

Abstract The uncertainty relations are discussed on a noncommutative plane when noncommutativity of momentum spaces is considered. It is possible to construct normalizable states by simultaneously saturating two coordinate-momentum uncertainty relations. However, under the natural condition θη ≪ 4ħ2 one can not construct a normalizable state by simultaneously saturating any other pairs out of four basic nontrivial uncertainty relations.

Open Physics•May 19, 2009•0 citations
In this paper, the Schrödinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space–space and space–momentum as well as momentum–momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.
In this letter, firstly, the Schrddoto\\ddot{o}ddotodinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space-space and space-momentum as well as momentum-momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.
We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the another one with usual commutative coordinates and momenta. We found connection between quadratic classical Hamiltonians, as well as Lagrangians, in their commutative and noncommutative regimes. The general procedure to compute Feynman's path integral on this noncommutative phase space with quadratic Lagrangians (Hamiltonians) is presented. Using this approach, a particle in a constant field, ordinary and inverted harmonic oscillators are elaborated in detail.