非对易相空间中各向同性谐振子的能级分裂

非对易空间的效应是出现在弦尺度下的一种物理效应. 本文介绍了量子力学非对易空间的代数关系; 讨论了非对易相空间中服从玻色-爱因斯坦统计的粒子的连续性条件, 最后给出了非对易相平面和非对易相空间中的线性谐振子的能级分裂.     

非对易相空间中角动量的分裂

非对易空间效应是一种在弦尺度下出现的物理效应. 本文首先介绍了在Schwinger表象中角动量的3个分量用产生--消灭算符的表示形式, 接着讨论了非对易相空间的量子力学代数; 然后用对易空间谐振子的产生-消灭算符表示出了在非对易情况下的角动量; 最后讨论了非对易相空间中角动量的分裂.     

非对易相空间中的狄拉克振子的能级和Wigner函数

非对易几何、弦论和圈量子引力理论的发展,使非对易空间受到越来越多的关注.非对易量子理论不同于平常的量子理论,它是弦尺度下的特殊的物理效应,处理非对易量子力学问题需要特殊方法.本文首先介绍了Moyal方程与Wigner函数,利用Moyal-Weyl乘法与Bopp变换将H(x,p)变换成^H(^x,^p),考虑坐标—坐标、动量—动量的非对易性,实现对非对易相空间中星乘本征方程的求解.并利用非对易相空间量子力学的代数关系,讨论了非对易相空间中狄拉克振子的Wigner函数和能级,研究结果发现非对易相空间中狄拉克振子的能级明显依赖于非对易参数.     

电磁场中带电粒子在非对易相空间的能级

非对易空间效应是出现在弦的尺度下的一种物理效应。 首先扼要介绍了非对易相空间中的量子力学代数、 Moyal Weyl乘法和广义Bopp变换, 然后讨论了电磁场中带电粒子的Hamiltonian算符, 最后给出了其在非对易相空间中的能级情况。     

非对易相空间中理想气体的热力学性质

首先从非对易相空间中重新确定微观状态个数和配分函数来讨论在非对易相空间中单原分子理想气体的热力学性质.结果显示非对易效应不能在理想气体系统的内能、物态方程、热容量等宏观热力学性质中测量出.然而发现系统的配分函数和熵发生变化,表示在非对易效应作用下系统的能量简并度和系统的无序度发生变化.     

非对易相空间中阻尼系统的Wigner函数

用量子力学来处理经典的阻尼系统,考虑到空间变量对易关系中包含的坐标-坐标和动量-动量的非对易性,利用Wigner函数在非对易相空间的基本性质,得到了阻尼谐振子在非对易相空间中的Wigner函数与对易空间及非对易空间的形式一致.     

非对易相空间中谐振子体系热力学性质的探讨

2000年以来, 有关非对易空间的各种物理问题一直是研究的热点, 并在量子力学、场论、凝聚态物理、天体物理等各领域中已被广泛地探讨. 采用统计物理方法讨论非对易效应对谐振子体系热力学性质的影响. 先以对易相空间中确定二维和三维谐振子的配分函数求出谐振子体系的热力学函数; 非对易相空间中的坐标和动量通过坐标-坐标和动量-动量之间的线性变换而以对易相空间中的坐标和动量来表示; 最终以非对易相空间中求出配分函数来讨论非对易效应对谐振子体系热力学性质的影响. 结果显示, 在非对易相空间中谐振子体系的配分函数和熵表达式均包含因非对易引起的修正项. 从分析结果得出如下结论: 非对易效应对谐振子的配分函数和熵函数等微观状态函数有一定的影响, 但对谐振子体系的内能、热容量等宏观热力学函数没有影响. 研究结果只是对应于满足玻尔兹曼统计的经典体系, 对于满足费米-狄拉克和玻色-爱因斯坦统计的量子体系需进一步推广研究.     

非对易相空间及其狄拉克粒子电磁场中的运动

近年来,有关非对易空间的各种物理问题成为诸多学者研究的热点,并在量子力学、量子场论、量子电动力学、凝聚态物理、天体物理等各领域中被广泛探讨.本文通过非对易空间里电磁场中狄拉克粒子的哈密顿量,推导出速度算符和所受到的力算符的表达式,利用Bopp变换方法给出了电磁场作用下的狄拉克粒子在非对易空间和非对易相空间中的哈密顿量,从而推导出了速度算符和力算符的表达式,其中均包含因非对易引起的修正项.在此基础上进一步分析得出,非对易效应对狄拉克粒子的速度算符和所受到的力算符有一定的影响,但动量-动量算符的非对易性对粒子的速度算符没有影响.     

非对易量子力学中中性原子在外电磁场中的朗道能级量子化

在非对易量子力学的框架中研究了中性原子在外加电磁场中运动时的朗道能级量子化问题.首先给出了中性原子体系在非对易量子力学中的哈密顿量,然后分别求解了非对易空间和非对易相空间中的薛定谔方程,并得到相应的朗道能级和本征波函数,同时给出了由于空间非对易性引起的能量修正项.     

非对易相空间三模坐标动量耦合谐振子的能谱

本文用不变本征算符方法研究非对易相空间中三模坐标动量耦合谐振子的能谱,分别得到了非耦合和坐标动量耦合两种情况下谐振子能谱的解析解,其中包括受非对易参数θ和φ影响的解λ0,1和λ1,1,以及不受非对易参数θ和φ影响的解λ0,2和λ1,2.然后,分析了两类耦合参数κ和η对三模坐标动量耦合谐振子能谱的影响.结果发现,耦合参数κ和η对λ1,1的影响是相同的,且当κ=η时,耦合系数κ和η对λ1,1是没有影响的.     

Dirac oscillator in noncommutative space

We study the Dirac oscillator problem in the presence of the Aharonov-Bohm effect with the harmonic potential in commutative and noncommutative spaces in S = V and S =-V symmetry limits. We calculate exact energy levels and the corresponding eigenfunctions by the Nikiforov-Uvarov(NU) method and report the impact of the spin and the magnetic flux on the problem. Helpful numerical data is included.     

Wigner function for the Dirac oscillator in spinor space

The Wigner function for the Dirac oscillator in spinor space is studied in this paper.Firstly,since the Dirac equation is described as a matrix equation in phase space,it is necessary to define the Wigner function as a matrix function in spinor space.Secondly,the matrix form of the Wigner function is proven to support the Dirac equation.Thirdly,by solving the Dirac equation,energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained.     

Wigner function for the Dirac oscillator in spinor space

The Wigner function for the Dirac oscillator in spinor space is studied in this paper. Firstly, since the Dirac equation is described as a matrix equation in phase space, it is necessary to define the Wigner function as a matrix function in spinor space. Secondly, the matrix form of the Wigner function is proven to support the Dirac equation. Thirdly, by solving the Dirac equation, energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained.     

Dirac oscillator in an external magnetic field

We show that (2+1)-dimensional Dirac oscillators in an external magnetic field is mapped onto the same with reduced angular frequency in absence of magnetic field. This can be used to study the atomic transitions in a radiation field. Relativistic Landau levels are constructed explicitly. Several interesting features of this system are discussed.     

System of interacting harmonic oscillators in rotationally invariant noncommutative phase space

Rotationally invariant space with noncommutativity of coordinates and noncommutativity of momenta of canonical type is considered. A system of N interacting harmonic oscillators in uniform field and a system of N particles with harmonic oscillator interaction are studied. We analyze effect of noncommutativity on the energy levels of these systems. It is found that influence of coordinates noncommutativity on the energy levels of the systems increases with increasing of the number of particles. The spectrum of N free particles in uniform field in rotationally invariant noncommutative phase space is also analyzed. It is shown that the spectrum corresponds to the spectrum of a system of N harmonic oscillators with frequency determined by the parameter of momentum noncommutativity.     

Dirac oscillator in perpendicular magnetic and transverse electric fields

We study (2+1)$(2+1)$ dimensional massless Dirac oscillator in the presence of perpendicular magnetic and transverse electric fields. Exact solutions are obtained and it is shown that there exists a critical magnetic field B_c$B_c$ such that the spectrum is different in the two regions B>B_c$B>B_c$ and B<B_c$B<B_c$. The situation is also analyzed for the case B=B_c$B=B_c$.     

Klein-Gordon oscillators in noncommutative phase space

We study the Klein-Gordon oscillators in non-commutative (NC) phase space. We find that the Klein-Gordon oscillators in NC space and NC phase-space have a similar behaviour to the dynamics of a particle in commutative space moving in a uniform magnetic field. By solving the Klein-Gordon equation in NC phase space, we obtain the energy levels of the Klein-Gordon oscillators, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly.     

Klein-Gordon oscillators in noncommutative phase space

We study the Klein-Gordon oscillators in non-commutative (NC) phase space.We find that the Klein-Gordon oscillators in NC space and NC phase-space have a similar behaviour to the dynamics of a particle in commutative space moving in a uniform magnetic field.By solving the Klein-Gordon equation in NC phase space,we obtain the energy levels of the Klein-Gordon oscillators,where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly.