On Quantum Mechanics on Noncommutative Quantum Phase Space

被引:0
作者
AEFDjema [1 ]
HSmail [2 ]
机构
[1] Abdus Salam International Centre for Theoretical Physics, Trieste,Italy
[2] Département de Physique,Institut d'Hydraulique,Centre Universitaire Mustapha Stambouli,Mascara ,Algeria
关键词
noncommutative space; quantum mechanics; Moyal product;
D O I
暂无
中图分类号
O413.1 [量子力学(波动力学、矩阵力学)];
学科分类号
070205 ; 0809 ;
摘要
<正> In this work,we develop a general framework in which Noncommutative Quantum Mechanics (NCQM),characterized by a space noncommutativity matrix parameter θ=∈jikθk and a momentum noncommutativity matrixparameter βij=∈ijkβk,is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed QuantumPhase Space (QPS).Imposing some constraints on this particular transformation,we firstly find that the product of thetwo parameters θ and β possesses a lower bound in direct relation with Heisenberg incertitude relations,and secondlythat the two parameters are equivalent but with opposite sign,up to a dimension factor depending on the physicalsystem under study.This means that noncommutativity is represented by a unique parameter which may play the roleof a fundamental constant characterizing the whole NCQPS.Within our framework,we treat some physical systems onNCQPS:free particle,harmonic oscillator,system of two-charged particles,Hydrogen atom.Among the obtained results,we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillatorwith Larmor frequency depending on β,representing the same particle in presence of a magnetic field (?)=q-1(?).For theother examples,additional correction terms depending on β appear in the expression of the energy spectrum.Finally,inthe two-particle system case,we emphasize the fact that for two opposite charges noncornmutativity is effectively feeledwith opposite sign.
引用
收藏
页码:837 / 844
页数:8
相关论文
共 3 条
[1]   Quantum mechanics as a matrix symplectic geometry [J].
Djemai, AEF .
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 1996, 35 (03) :519-556
[2]  
C. N. Yang. Phys Rev . 1947
[3]  
A.Smailagic,E.Spallucci. Phys.Rev.D . 2002