非对易空间平移算符及其正交归一完备态集合  

Translation operator in noncommutative space and a set of complete states of orthogonality and normalization

作　　者：温俊青[1] 石康杰[2] 

机构地区：[1]西安石油大学理学院,陕西西安710065 [2]西北大学现代物理研究所,陕西西安710069

出　　处：《西北大学学报（自然科学版）》2006年第2期221-224,230,共5页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(10575080)

摘　　要：目的研究相空间面积为A(整数)的一般格点上的平移态组成完备集合,讨论了一个任意态按照这组完备集展开的展开系数及其正交归一条件。方法运用H．Bacy等人的方法,通过将非对易空间的平移算符作用于几个一般的态矢上,构造了Hilbbert空间的完备集合{|φmnj>}。结果通过构造完备集合{|φmnj>},求出了一个任意态|ψ)按照上述完备集展开的展开系数,讨论了这组完备集的正交归一条件。结论在研究非对易环(torus)时,用{|φmnj>}做基矢是特别方便的。这些基矢对于研究非对易环的旋转及非对易空间的场论中的孤子解都有意义。本文的研究结果也可以进一步推广到2n维非对易空间。Aim To study translation states located in phase space square A （integral） on a general lattice to construct a set of complete states, and discuss the expansion coefficient of a random state in terms of the set of complete states expansion and the condition of their orthogonality and normalization. Methods Making use of the methods of H. Bacy and other people, by translation operator in noncommutative space operating some general states construct a set of complete states {｜Φmnj〉} in Hilbbert space. Results Solving the expansion coefficient of a random state in terms of above set of complete states expansion by constructing a set of complete states {｜Φmnj〉} and discussing the condition of their orthogonality and normalization. Conclusion Making use of a set of complete states as basis vector when the study of noncommutative ring is very convenient. It is significant to study the circumgyration of noncommutative ring （torus） and soliton solution of field theory on noncommutative space. The results can be generalized 2n dimension noncommutative space.

关 键 词：平移算符 完备态集合 非对易空间 相干态 kq表象 

分 类 号：O432.1[机械工程—光学工程]