有限维q非谐振子广义相干态振幅N次方压缩

利用Zhang等人提出的单模辐射场的振幅N次方压缩理论,研究了有限维希尔伯特空间中单参数q变形非简谐振子广义相干态的振幅N次方压缩效应.结果发现:该量子光场的确存在场的振幅N次方压缩效应,其压缩条件分别与相位角Φ、维度参数s、压缩幂次N、平均光子数的方根r和变形参数q相关;这一结果与无限维希尔伯特空间单参数q变形广义相干态的情形截然不同.     

Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schrodinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special eases like （i） a confined free particle, （ii） a confined time-independent harmonic oscillator, and （iii） an aging oscillator are examined, and the corresponding time- dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some parametric moving boundaries as well.     

带电谐振子在非均匀外场中的非对易能级

非对易空间的量子效应是出现在弦的尺度下的一种物理效应．从Moyal—Weyl乘法与Bopp变换出发,利用了非对易相空间的量子力学代数关系;在考虑坐标一坐标非对易性的情况下,讨论了非对易空间中带电谐振子在非均匀外场中的Hamiltonian,并且给出了相应的能级．     

双模耦合谐振子哈密顿量的一般解法

双模耦合谐振子哈密顿量是广义坐标■和广义动量■的一般二次型,通过一个坐标变换可以将其表示为新基底下的标准二次型,经计算得知,新基底之间满足准正则对易关系,从而引入准粒子的产生和湮没算符,这样就消除了耦合项,哈密顿量化简成为双模独立谐振子情形,使问题得到解决.这样的解决方法可以推广到各向异性n模谐振子的耦合体系.     

Solving Dirac Equation with New Ring-Shaped Non-Spherical Harmonic Oscillator Potential

A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 （2005） 94. The positive energy states of system are discussed and the conclusions are made properly.     

多粒子多空穴能态密度的谐振子模型计算

在严格考虑了泡利不相容原理的前提下,导出了任意单粒子哈密顿量下多粒子多空穴态的能态密度的一般性精确公式;并应用半经典的Thomas-Fermi近似,计算了三维线性谐振子下的能态密度;计算了g_1p至g_10p,g_1h至g_7h以及g_1p－1h至g_6p－6h能态密度;讨论了泡利不相容的影响,与微子模型中通用的等间隔模型的能态密度进行了比较.由计算结果看出,激子模型中通用的等间隔单粒子能级密度模式在由核子诱发的核反应中,是一很好的近似.     

硅微机械谐振器特性与激励光斑位置关系的研究

阐述了对硅悬臂梁谐振子进行光激励研究的结果，结果表明，谐振子的振幅与激励光斑的位置以及所激励的模态有关，在模态的两节点的中心位置进行激励，可得到最大的振幅，而且振幅随着激励光斑偏离子中心位置而下降基节点处激励时，振幅达到最小。上述结论也适用于其它点热源激励的微机械谐振器，并为点热激激励的微机械谐振器的设计和制作提供了依据。     

扩展的谐振子Feynman公式及其应用

本文给出谐振子包含极点和超越极点的扩展Feynman传播子公式的新推导。我们应用了传播子的本征函数展开,从而揭示出Maslov修正和本征函数字称的关系。这一扩展的 Feynman公式被用来讨论在稳恒均匀磁场中和有Chern-Simon背景规范场存在时迴旋运动带电粒子Feynman传播子位相修正及其物理效应。     

Bose—Einstein Condensation in a Spherical Symmetric Harmonic Trap

Using a perturbation theory approach,we derive an approximate analytical solution of the Gross-Pitaevskii equation in a spherical symmetric harmonic trap.This solution is consistent with that obtained numerically.