坐标依赖的非对易空间及其空间中的谐振子和超对称谐振子（英文）  

Harmonic Oscillator and Supersymmetric Harmonic Oscillator on Coordinate Dependent Noncommutative Space

作　　者：库尔班.卡依木 沙依甫加马力.达吾来提 买买提阿布都拉.艾克木 

机构地区：[1]新疆大学物理科学与技术学院,新疆乌鲁木齐830046 [2]和田师范专科学校物理系,新疆和田848000

出　　处：《新疆大学学报（自然科学版）》2016年第1期69-73,共5页Journal of Xinjiang University(Natural Science Edition)

基　　金：National Natural Science Foundation of China(11165014 and 11465018)

摘　　要：本文讨论了以SU(2)类型非对易代数[x_i,x_j]=i∈_(ijk)x^k作为代数的坐标依赖的非对易空间及其空间中的三位谐振子和三维超对称谐振子.首先计算了三位谐振子因非对易性而引起的修正.结果显示,三位谐振子在这非对易空间中会得到角动量有关的能级.然后用超对称系统的实现方法建立了超对称谐振子系统并给出了其对应的哈密顿算符在对易空间中的表达式.经过分析超对称哈密顿算符的表达式可知此系统因为所选取的SU(2)类型非对易代数而会产生磁偶极子效应.A three dimensional harmonic oscillator and it＇s supersymmetric analogue on coordinate dependent non- commutative space defined by a su（2） type noncommutative algebra [xi , xj ] = iεijkyxk were discussed. At first, the energy corrections of harmonic oscillator due to noncommutativity were calculated, the result shows that harmonic oscillator ob- tains angular momentum related extra energy spectrum. Then, the hamiltonian of supersymmetric analogue of oscillator system on noncommutative space were obtained. Analyzing the supersymmetric hamiltonian, it shows that the system generates magnetic dipole interaction automatically as a direct consequence of this su（2） type noncommutative algebra.

关 键 词：非对易空间 谐振子 超对称 

分 类 号：O413.13[理学—理论物理]