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Exact solution to two-dimensional isotropic charged harmonic oscillator in uniform magnetic field in non-commutative phase space 总被引:1,自引:0,他引:1
In this paper,the isotropic charged harmonic oscillator in uniform magnetic field is researched in the non-commutative phase space;the corresponding exact energy is obtained,and the analytic eigenfunction is presented in terms of the confluent hypergeometric function.It is shown that in the non-commutative space,the isotropic charged harmonic oscillator in uniform magnetic field has the similar behaviors to the Landau problem. 相似文献
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由牛顿第二定律得到二维各向同性带电谐振子在均匀磁场中运动的运动微分方程,通过对运动微分方程的直接积分得到系统的两个积分(守恒量).利用Legendre变换建立守恒量与Lagrange函数间的关系,从而求得系统的Lagrange函数,并讨论与守恒量相应的无限小变换的Noether对称性与Lie对称性,最后求得系统的运动学方程. 相似文献
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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. 相似文献
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In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity. First, new Poisson brackets have been defined in non-commutative phase space. They contain corrections due to the non-commutativity of coordinates and momenta. On the basis of this new Poisson brackets, a new modified second law of Newton has been obtained. For two cases, the free particle and the harmonic oscillator, the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys. Rev. D, 2005, 72: 025010). The consistency between both methods is demonstrated. It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space, but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative. 相似文献
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二维各向同性变频率谐振子的超对称性及其不变量的超对称量子力学精确解 总被引:1,自引:0,他引:1
采用超对称量子力学与不变量相结合的方法讨论了二维各向同性变频率谐振子,给出了二维各向同性变频率谐振子的不变量,采用超对称量子力学方法精确求解了不变量的本征值和本征函数,并且给出了当频率恒定时,二维常频率谐振子的本征值和本征函数的精确解.最后对不变量的超对称性进行了讨论. 相似文献
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In the non-commutative space, wave functions and geometric phases are derived for the time-dependent harmonic oscillator in external time-dependent magnetic and electric field. Explicit forms of the coherent states are also given, which are not the minimum uncertainty states for the coordinates and momenta. 相似文献
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三维各向同性谐振子的代数解法 总被引:1,自引:0,他引:1
用带角动量的玻色算子统一构成三维各向同性谐振子的能量本征函数,并讨论了它们和直接求解微分方程得到的本征解之间的关系.这种方法快捷优美,而且有统一的表达式和简单的李代数关系。 相似文献
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In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space.The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity.First,new Poisson brackets have been defined in non-commutative phase space.They contain corrections due to the non-commutativity of coordinates and momenta.On the basis of this new Poisson brackets,a new modified second law of Newton has been obtained.For two cases,the free particle and the harmonic oscillator,the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys.Rev.D,2005,72:025010).The consistency between both methods is demonstrated.It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space.but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative. 相似文献
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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. 相似文献
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根据Laguerre多项式的积分公式,在考虑了哈密顿量中正比于B~2项影响的情况下,导出了均匀磁场中三维各向同性谐振子微扰矩阵元的普遍表达式,并指出n=3能级的简并度完全解除. 相似文献
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文中得到d维各向同性谐振子归一化径向波函数. 在径向基本算子r,(1)/(r),(d)/(dr)的基础上,可以直接构造d维各向同性谐振子的四类升降算子,同时也得到它们的归一化系数. 相似文献
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本文应用拉普拉斯变换得到了三维各向同性谐振子波函数边界的精确解,同时,利用同种方法还得到了利用产生算符和湮灭算符表达的该波函数的递推关系. 相似文献
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We explore the non-commutative (NC) effects on the energy spectrum of a two-dimensional hydrogen atom. We consider a confined particle in a central potential and study the modified energy states of the hydrogen atom in both coordinates and momenta of non-commutativity spaces. By considering the Rashba interaction, we observe that the degeneracy of states can also be removed due to the spin of the particle in the presence of NC space. We obtain the upper bounds for both coordinates and momenta versions of NC parameters by the splitting of the energy levels in the hydrogen atom with Rashba coupling. Finally, we find a connection between the NC parameters and Lorentz violation parameters with the Rashba interaction. 相似文献
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李玉山 《原子与分子物理学报》2015,32(6):481-486
采用截断求和法和半经典近似,以二维理想玻色气体为例,研究了磁场和简谐势阱中低维荷电自旋-1玻色子的相变及磁性质.结果表明,电荷-磁场和自旋-磁场作用的竞争导致玻色-爱因斯坦凝聚临界温度随磁场的增大先略微上升后缓慢下降.截断求和法能够有效的改进半经典近似的不足.最后,讨论了磁化强度由抗磁性到顺磁性的转变及自旋因子临界值随磁场和温度的变化. 相似文献
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