Formulation, interpretation and application of non-commutative quantum mechanics

被引:102
作者
Scholtz, F. G. [1 ,2 ]
Gouba, L. [2 ]
Hafver, A. [1 ]
Rohwer, C. M. [1 ]
机构
[1] Univ Stellenbosch, Inst Theoret Phys, ZA-7600 Stellenbosch, South Africa
[2] Stellenbosch Inst Adv Study, NITheP, ZA-7600 Stellenbosch, South Africa
基金
新加坡国家研究基金会;
关键词
HARMONIC-OSCILLATOR; REPRESENTATION; CONSEQUENCES; SPECTRUM;
D O I
10.1088/1751-8113/42/17/175303
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert Schmidt operators acting on non-commutative configuration space. It is argued that the standard quantum mechanical interpretation based on positive operator valued measures, provides a sufficient framework for the consistent interpretation of this quantum system. The implications of this formalism for rotational and time reversal symmetry are discussed. The formalism is applied to the free particle and harmonic oscillator in two dimensions and the physical signatures of non-commutativity are identified.
引用
收藏
页数:13
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