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arXiv:0902.3782 · Physics Letters A

A new kind of representations on noncommutative phase space

Sicong Jing, Bing-Sheng Lin

Published Oct 30, 2008• 14 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2008.10.052

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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 Schddoto\\ddot{o}ddotodinger equation from noncommutative space to commutative space is obtained.
The structure of the state-vector space of identical bosons in noncommutative spaces is investigated. To maintain Bose–Einstein statistics the commutation relations of phase space variables should simultaneously include coordinate-coordinate non-commutativity and momentum-momentum non-commutativity, which leads to a kind of deformed Heisenberg-Weyl algebra. Although there is no ordinary number representation in this state-vector space, several set of orthogonal and complete state-vectors can be derived which are common eigenvectors of corresponding pairs of commuting Hermitian operators. As a simple application of this state-vector space, an explicit form of two-dimensional canonical coherent state is constructed and its properties are discussed.