Raman自由电子激光的半经典理论

采用Ｔｈｏｍａｓ-Ｆｅｒｍｉ近似势，将多电子系统简化为单电子问题，并用微扰论求解了Ｋｌｅｉｎ-Ｇｏｒｄｏｎ方程．由电子的零级波函数求得了电荷密度和电流密度的零级表达式．通过适当简化Ｋｌｅｉｎ-Ｇｏｒｄｏｎ方程，用分离变量和ＷＫＢ近似，求得了电子波函数及相应的电荷密度与电流密度的表达式 关键词：     

二维氢原子径向方程的两种解法

本文利用两种方法求解二维氢原子的径向方程：一是升降算符法，由所定义的关于量子数ｍ的升降算符，给出了径向波函数之间的递推公式，求出了二维氢原子的能级和径向波函数的表达式；二是通过与三维氢原子径向方程的类比，在三维氢原子径向波函数的基础上，直接给出了二维氢原子径向波函数的一般表示式．两种解法所得结果完全一致．     

氢原子径向波函数的“初等”解法

用构造氢原子径向波函数的方法,通过解薛定谔方程给出氢原子径向波函数幂多项式的系数．     

氢原子和谐振子的能级、波函数的联系

求氢原子和谐振子的能级、波函数是解两个不同的定态薛定谔方程的问题。实际上，我们从三维谐振子的径向方程出发，应用适当的变换，就能由三维谐振子的能级和波函数导出氢原子与类氢离子的能级和波函数．     

一类环状非球谐振子势场中相对论粒子的束缚态解

提出了一种新的环状非球谐振子势, 在标量势与矢量势相等的条件下，给出了其Klein-Gordon方程和Dirac方程的束缚态解. Klein-Gordon方程的θ角向波函数以超几何函数表示，径向波函数可用合流超几何函数或广义拉盖尔多项式表示，能谱方程由径向波函数满足的束缚态边界条件得到. Dirac方程的旋量波函数可用Klein-Gordon方程的解构造. 关键词： 环状非球谐振子势 Klein-Gordon方程 Dirac方程 束缚态     

Makarov势的Dirac方程的束缚态解

给出了Makarov型标量势与矢量势相等条件下的Dirac方程的束缚态解. Dirac方程的角向方程用因子分解方法求解，在得出角向波函数的过程中，自然地得到了属于同一本征值的不同角向波函数间的递推操作. 径向束缚态波函数用合流超几何函数表示，束缚态的能量方程可由径向波函数满足的边界条件得到. 关键词： Makarov势 Dirac方程 束缚态 因子分解方法     

薛定谔方程的解在r=0邻域的行为

本文对中心力场中Ｓｃｈｒｏｄｉｎｇｅｒ方程径向方程的解在ｒ＝０邻域的行为作了仔细分析．根据波函数的统计诠释，仔细讨论了与指标方程的两根相应的解的取舍，澄清了一些量子力学教科书中不妥当的讲法．     

氘核的相对论波函数

假设氘核的相对论波函数满足场论中的Bethe-Salpeter方程,在质心系瞬时作用的近似下推导了氘核波函数所满足的耦合方程,并简单的讨论了氘核波函数的一些性质。瞬时作用的引进给波函数的旋量结构以很强的限制使波函数分量的数目减少了,并且把求解四维空间B-S方程的问题化为在质心系三维空间中的求解,物理意义明确便于计算和讨论。定性估计给出与S波相比P波约是(?)量级的一个小量。     

修正Pschl-Teller势的薛定谔方程束缚态的一种解法

用一个新的变换求解了修正Ｐｓｃｈｌ－Ｔｅｌｅｒ势的薛定谔方程束缚态,得到了能量本征值及相应的波函数．     

双环形Coulomb势Schroedinger方程束缚态的精确解

双环形Coulomb势是指在氢原子势外面再加上一个双环形平方反比势。该模型势是在讨论类似于苯环分子结构的基础上提出的，该模型势在分子和原子物理中有着广泛的应用．本文研究了双环形Coulomb势Schroedinger方程的束缚态精确解，所采用的方法是首先对双环形Coulomb势的Schroedinger方程在球坐标系中进行分离变量，得到相应的角向方程和径向方程；证明双环形Coulomb势在角向和径向具有超对称性和形不变性；根据超对称性和形不变性的性质，获得了角动量量子化条件和束缚态的能谱方程，并将归一化角向波函数用Jacobi多项式表示，将归一化径向波函数用Laguerre多项式函数表示．体系的波函数和束缚态能谱性质由三个量子数n、m和s及势参数a，a和b描述．本文说明量子物理中一些具有对称性的非中心势有精确解．用超对称性和形不变性方法还可以讨论其他形式的非中心势．     

Evaluation of critical current based on a new transition concept

The critical current of high-temperature superconductor (HTS) tapes depends on temperature, magnetic field, and flux angle against the tape. Analyzing the performance of an HTS coil relies on the critical current equation, which has these dependencies. To date, the critical current equation has been obtained by fitting the measured data. However, this fitting method requires the time-consuming and laborious work of measuring the tapes. In this study, based on a new transition concept in applying a magnetic field, we show how to obtain the critical current equation, while keeping the temperature constant. From the wave function of the Cooper pair which distributes along a magnetic flux quantum, a wave function at the transition state is obtained; this yields the wave functions with perpendicular and parallel magnetic components against the tape. Combining these wave functions yields the conclusive critical current density equation. To confirm the accuracy of this equation, used Bi-2223/Ag tapes, it was compared with the measured critical current under various magnetic fields and flux angles; it was found that they agree well. The parameters of this equation can be obtained by measuring the perpendicular/parallel critical magnetic field component. This equation does not require fitting the measured data, therefore, it can be employed with any Bi-2223/Ag tape.     

Dirac Quantization in Kantowski—Sachs Spacetime

By forming the square root of the Wheeler-DeWitt equation and applying itto a minisuperspace composed of a Kantowski-Sachs universe, we derive acosmological wave function with conserved current and positive-definiteprobability density.     

Phenomenology of current oscillations by sliding charge density waves

Bardeen's suggestion that the dc current associated with the sliding of a charge density wave instead of the dc electric field determines the dynamics of the phase, is formulated in a simple but self-consistent way. The resulting equation of motion for the phase reduces to that of the classical model of a rigid charge density wave far above threshold with a new, nondissipative scaling frequency. It is suggested that the harmonic content of the narrow band noise monitored as function of dc bias may decide between both interpretations. The model may also have relevance to the observation of subharmonics and chaos in charge density wave systems.     

托卡马克等离子体不同平衡位形下的电子回旋波电流驱动

在给定的等离子体总电流和中心电流密度条件下,数值求解平衡方程,求出不同拉长比和三角形变因子的托卡马克等离子体温度、密度、磁场分布,然后通过求解波迹方程和Fokker-Planck方程,分别计算这些位形下的电子回旋波波迹和电流驱动.结果表明：电子回旋波X模从顶部发射时,随着拉长比的增大,波迹会向弱场侧偏移.电子回旋波X模从弱场侧发射时,电子回旋波在等离子体中传播沉积的功率份额随着拉长比的增大而增加,驱动电流位置随着三角形变因子的增大向等离子体中心移动.驱动电流位置随环向和极向发射角的减小向中心移动,对应的电流密度峰值也变大.     

Quantum mechanics as applied mathematical statistics

Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schrödinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.     

发射波功率密度对电子回旋波电流驱动的影响

采用高斯光束的研究方法,结合Fokker-Planck方程,在堆级等离子体条件下模拟了发射波功率密度的改变对电子回旋波功率沉积以及电流驱动的影响。结果表明,高功率密度的波束会拓宽功率沉积剖面,使功率沉积的位置略有外移,电流驱动效率略有降低。     

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采用高斯光束的研究方法,结合Fokker-Planck方程,在堆级等离子体条件下模拟了发射波功率密度的改变对电子回旋波功率沉积以及电流驱动的影响。结果表明,高功率密度的波束会拓宽功率沉积剖面,使功率沉积的位置略有外移,电流驱动效率略有降低。     

The repulsive nature of naked singularities from the point of view of Quantum Mechanics

We use the Dirac equation coupled to a background metric to examine what happens to quantum-mechanical observables like the probability density and the radial current in the vicinity of a naked singularity of the Reissner–Nordström type. We find that the wave function of the Dirac particle is regular in the point of the singularity. We show that the probability density is exactly zero at the singularity reflecting quantum-mechanically the repulsive nature of the naked singularity. Furthermore, the surface integral of the radial current over a sphere in the vicinity of the naked singularity turns out to be also zero.     

Scattering of a Klein-Gordon particle by a black hole

By using the curved space-time Klein-Gordon equation, the form of the wave function of a scalar particle near a nonrotating black hole is obtained. It is shown that although the radial wave function oscillates infinitely rapidly near the black hole, the probability density remains finite even on the event horizon. This is consistent with the fact that the Schwarzschild surface is nonsingular. An expression is given for the large angular momentum scattering differential cross section by comparing the asymptotic form of the radial wave equation with the corresponding Coulomb radial wave equation in ordinary quantum mechanics.