二维各向同性谐振子径向矩阵元的递推关系

推导出二维各向同性谐振子径向矩阵元〈nm|ρ^q|n′m′〉所满足的递推关系.     

弱组态相互作用对SiⅫ光学允许跃迁谐振子强度的影响

本文把组态相互作用波函数展开成解析的Slater-型轨道形式,利用程序CIV3计算了SiⅫ的单组态和多组态能级和谐振子强度。结果表明,组态相互作用对能级影响很小,但对谐振子强度的影响却很大。对于初末两态主量子数不同的跃迁,组态相互作用对长度规范下的谐振子强度影响较大;而对于初末两态主量子数相同的跃迁,组态相互作用对速度规范下的谐振子强度影响较大。文中还对产生这种现象的原因进行了讨论,并把我们的结果与实验以及其它理论结果进行了比较。     

环形非球谐振子径向矩阵元的通项公式及其递推关系

环形非球谐振子的势能函数为V(r,θ)=12mω2r2+22mAr2+22mbr2sin2θ,其精确的能谱方程和归一化的波函数已经获得.在此基础上,给出了环形非球谐振子径向矩阵元的通项公式和不同幂次径向矩阵元之间所满足的递推关系.作为特例,讨论了球谐振子、非球谐振子和环形振子的有关结果. 关键词： 环形非球谐振子 径向矩阵元 通项公式 递推关系     

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

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．     

Thermal state of the general time-dependent harmonic oscillator

Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic oscillator. The uncertainty relation of the system is always larger than ħ/2 not only in number but also in the thermal state as expected. We used the diagonal elements of density operator satisfying Leouville-von Neumann equation to calculate various expectation values in the thermal state. We applied our theory to a special case which is the forced Caldirola-Kanai oscillator.     

Wave function of the harmonic oscillator in classical statistical mechanics

The notion of wave function of the classical harmonic oscillator is discussed. The evolution equation for this wave function is obtained using the classical Liouville equation for the probability-distribution function of the harmonic oscillator. The tomographic-probability distribution of the classical oscillator is studied. Examples of the ground-like state and the coherent state of the classical harmonic oscillator are considered.     

Classical mechanics in non-commutative phase space

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.     

Dynamical Lie algebraic treatment for the A+BC scattering

We report the study of translational‐vibrational energy transfer in the A+BC scattering using the dynamical Lie algebraic approach combined with the intermediate picture. The rotational sudden approximation is applied to treat the rotational motion of the BC molecule, which is regarded as an anharmonic oscillator. The calculated results show that the transition probabilities increase with increasing rotational quantum number. Comparison with those obtained in the collinear collision of system A+BC manifests that the transition probabilities here increase indeed. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 214–221, 2001     

高功率中红外3.8 μm激光器

 采用1.06 μm激光泵浦准相位匹配周期极化铌酸锂（PPMgLN）晶体光参量振荡器,实现高功率高效率高重复频率3.84 μm中红外激光输出。泵浦源为椭圆光斑1.06 μm激光,PPMgLN晶体MgO摩尔分数为5%,光参量振荡器为外腔单谐振结构,采用e→e+e相位匹配,利用了PPMgLN晶体的最大非线性系数。在1.06 μm激光功率为73 W,声光Q开关工作频率为7.5 kHz的条件下,获得平均功率8.3 W,波长3.84 μm激光输出,光-光转换斜率效率14.1％,水平和垂直方向光束质量平方因子分别为1.94,4.57。     

一种新型的用于差分吸收激光雷达中脉冲式光学参量振荡器的种子激光器的频率稳定方法

提出了一种新型的用于差分吸收激光雷达中脉冲式光学参量振荡器的种子激光器的频率稳定方法. 详细介绍了该稳频方法的工作原理和实验装置, 并在理论上对该方法的稳频精度及其影响因素进行了分析. 利用该方法, 在实验中将种子光激光器稳定在水汽的吸收峰中心(935.6849 nm)处, 频率抖动的标准差小于8 MHz. 测试了种子注入后的光学参量振荡器输出的脉冲光的频率抖动, 测试结果表明, 脉冲光频率能够与种子光保持一致, 频率抖动的标准差小于28.7 MHz, 该稳频结果完全能够满足差分吸收激光雷达的需求.