氢原子的固有电偶极矩

用经典力学和双波量子力学计算了氢原子的固有电偶极矩。双波量子理论算得的结果在经典极限下与经典力学的结果一致。普通量子力学对氢原子Stark效应中表现出来的电偶极矩难以做出很好的解释，因为一个波函数描述的是系综而不是单个粒子。经典力学和双波量子力学可描述单个粒子的行为，对永久电偶极矩的计算和解释显得自然而合理。     

二维氢原子的双波描述

运用双波量子理论,给出了二维氢原子的双波函数描述,并讨论了其经典极限.结果表明,双波函数描述单个粒子的运动状态,并将通常的量子力学描述结果作为系综统计平均值包含在其中. 关键词：     

双波量子理论中的守恒定律

研究了双波量子理论中守恒定律的数学形式,讨论了三维各向同性谐振子的守恒量及其经典极限.结果表明,双波量子理论中的守恒定律适用于单个粒子,而通常量子力学中的守恒定律仅适用于统计系综. 关键词：     

均匀磁场中带电粒子运动的双波描述

用双波量子理论描述带电粒子在均匀磁场中的运动,得到对单个粒子运动状况的完全描述。在任何时刻都能说出任一力学量的确切数值。通常量子力学中的概率性和平均值公式来源于双波描述对某类系综的平均结果。量子力学中的规范变换特性也能由系综平均看出。 关键词：     

在均匀强磁场中氢原子塞曼效应久期方程的简化公式

在均匀强磁场中,当氢原子的哈密顿量中B2项不能忽略时,氢原子的库仑场对称性遭到破坏,能级简并被全部解除.在应用变分法和数值法计算氢原子的能级过程中,计算十分复杂,而应用微扰法求解氢原子的能级,存在解久期方程的n2高阶行列式的困难.本文应用简并态微扰理论和球谐函数的性质,得到久期方程中非零微扰矩阵元普遍表达式.根据非零微扰矩阵元普遍表达式的性质,可以将氢原子塞曼效应久期方程的n2高阶行列式分解成1阶到n阶共n个低阶行列式的乘积,得到氢原子塞曼效应久期方程的简化公式,使得求解均匀强磁场中氢原子塞曼效应能级过程简化.而且由该公式可以得到氢原子在低能态时塞曼效应能级的解析解.根据该久期方程的简化公式计算了n=3氢原子塞曼效应一级近似能级.     

同向电磁场中氢原子低能级简并的解除

利用同向电磁场的作用使氢原子低能级简并完全解除.     

二维各向同性谐振子几种解的比较

在二维各向同性谐振子中，除哈密顿量外还有三个独立的守恒量，因此，这体系有三种定态解。这三种解有两种是大家熟知的，这第三种解在本文给出了，这三种本征解描述三种不同的系综。应用中根据什么考虑在三种解中选择一种在本文中也作了讨论。     

氢原子及类氢原子的双波描述

采用双波量子理论对氢原子及类氢原子进行了双波函数描述，讨论了其经典极限。证明了双波函数满足波函数的归一化条件。在双波函数描述下，能量和角动量F的平均值为En和mh。同时求出了r，cosθ,sinθ,cosψ，sinψ和X，Y，Z在双波函数描述的平均值。对力学量f求统计平均值的结果表明，单波函数描述的是氢原子及类氢原子系统的运动状况。只有双波函数描述的是单个粒子的运动状况。     

三平行光子晶体单模波导的耦合特性及其应用

将三光子晶体单模波导的相互耦合看成一个多模干涉系统.本征模的色散曲线相交或近于相交并出现简并模，简并模之间存在强烈耦合并导致模式的分布方式发生转变.多模干涉系统中，不同波长的光波能量在传输过程中由于相干而具有不同的空间输出行为，在近简并点处多模之间的相干解除，能流限制在原输入方向，不发生转移.三光子晶体单模光波导的这种特性可用来制作波分复用或解复用器件. 关键词： 光子晶体波导 简并模 多模干涉 波分复用或解复用     

拓扑反能带理论

<正>1拓扑能带理论能带理论是量子力学在固体材料中的一次伟大应用,催生了半导体和半导体激光等发明,促进了第三次工业革命。根据量子力学,我们知道原子中的电子只能处于离散的能级。如果原子之间的距离很远,那么电子被束缚在各自的原子核附近,原子系综存在大量的相互独立的简并能级。     

氢原子问题的试探解法

本文给出一种初等解法（试探解法），用以求出氢原子束缚态的定态波函数及能量、角动量平方与角动量第三分量的量子化条件     

When Langmuir is too simple: H2 dissociation on Pd(111) at high coverage

Recent experiments of H2 adsorption on Pd(111) [Nature (London) 422, 705 (2003)]] have questioned the classical Langmuir picture of second order adsorption kinetics at high surface coverage requiring pairs of empty sites for the dissociative chemisorption. Experiments find that at least three empty sites are needed. Through density functional theory, we find that H2 dissociation is favored on ensembles of sites that involve a Pd atom with no direct interaction with adsorbed hydrogen. Such active sites are formed by aggregation of at least 3 H-free sites revealing the complex structure of the "active sites."     

Some comments on quasi-bound-state calculations

Quasi-bound-state energy calculations are made for a perturbed oscillator and a perturbed hydrogen atom. The theory of the least-squares method is analysed. A simple numerical variant of the well-known stabilization method is tested, and the results are compared with those from the least-squares and perturbation-series methods.     

Quantization effects in the plasma universe

It is suggested that a unification of the morphology of the solar system, anomalous intrinsic red shifts of quasars and galaxies, the structure of the hydrogen atom, the Einstein equations of general relativity, and Maxwell's equations can be accomplished by a basic consideration of the minimum-action states of cosmic and/or virtual vacuum field plasmas. A formalism of planetary formation theory leads naturally to a generalization which describes relativistic gravitational field theory in terms of a `pregeometry'. A virtual plasma associated with the vacuum state is postulated. It is demonstrated that the relaxed state of the virtual plasma underlies Einstein's field equation and predicts the proper form for the effective gravitational potential generated by the Schwarzschild solution of those equations. A further extension of the theory demonstrates that it also predicts the structure of the hydrogen atom described in terms of the Schrodinger equation of quantum mechanics. These concepts are applied in an attempt to explain the quantized anomalous red shifts in related galaxies as observed by H. Arp and J.H. Sulentic (1985). A possible unified field theory is suggested based on the above-mentioned concepts     

Noncommutative point sources

We construct a perturbative solution to classical noncommutative gauge theory on R3 minus the origin using the Groenewald-Moyal star product. The result describes a noncommutative point charge. Applying it to the quantum mechanics of the noncommutative hydrogen atom gives shifts in the 1S hyperfine splitting which are first order in the noncommutativity parameter.     

Thermodynamic theory of equilibrium fluctuations

The postulational basis of classical thermodynamics has been expanded to incorporate equilibrium fluctuations. The main additional elements of the proposed thermodynamic theory are the concept of quasi-equilibrium states, a definition of non-equilibrium entropy, a fundamental equation of state in the entropy representation, and a fluctuation postulate describing the probability distribution of macroscopic parameters of an isolated system. Although these elements introduce a statistical component that does not exist in classical thermodynamics, the logical structure of the theory is different from that of statistical mechanics and represents an expanded version of thermodynamics. Based on this theory, we present a regular procedure for calculations of equilibrium fluctuations of extensive parameters, intensive parameters and densities in systems with any number of fluctuating parameters. The proposed fluctuation formalism is demonstrated by four applications: (1) derivation of the complete set of fluctuation relations for a simple fluid in three different ensembles; (2) fluctuations in finite-reservoir systems interpolating between the canonical and micro-canonical ensembles; (3) derivation of fluctuation relations for excess properties of grain boundaries in binary solid solutions, and (4) derivation of the grain boundary width distribution for pre-melted grain boundaries in alloys. The last two applications offer an efficient fluctuation-based approach to calculations of interface excess properties and extraction of the disjoining potential in pre-melted grain boundaries. Possible future extensions of the theory are outlined.     

Noncommutative quantum mechanics from noncommutative quantum field theory

We derive noncommutative multiparticle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Particles of opposite charges are found to have opposite noncommutativity. As a result, there is no noncommutative correction to the hydrogen atom spectrum at the tree level. We also comment on the obstacles to take noncommutative phenomenology seriously and propose a way to construct noncommutative SU(5) grand unified theory.     

Foundations of the quantum statistics of systems in equilibrium: A measuretheoretic approach

The fundamental equations of equilibrium quantum statistical mechanics are derived in the context of a measure-theoretic approach to the quantum mechanical ergodic problem. The method employed is an extension, to quantum mechanical systems, of the techniques developed by R. M. Lewis for establishing the foundations of classical statistical mechanics. The existence of a complete set of commuting observables is assumed, but no reference is made a priori to probability or statistical ensembles. Expressions for infinite-time averages in the microcanonical, canonical, and grand canonical ensembles are developed which reduce to conventional quantum statistical mechanics for systems in equilibrium when the total energy is the only conserved quantity. No attempt is made to extend the formalism at this time to deal with the difficult problem of the approach to equilibrium.     

氢同位素转动跃迁拉曼频移的理论计算

激光拉曼光谱作为一种非侵入式的物质结构和成分分析的测试手段特别适合于核工业中含氚放射性同位素气体的定性和定量分析。将经典物理学方法和量子力学理论相结合,采用非刚性转子校正模型,计算获得了H2、HD、HT、D2、DT、T26种氢同位素气体分子的转动跃迁拉曼频移,为氢同位素气体拉曼光谱谱峰的辨识提供理论数据。通过实验测定H2和D2的转动拉曼光谱,得到这2种分子的转动拉曼图谱和拉曼频移,并将测定结果与计算结果进行比较,验证了理论计算方法的可行性和正确性。