经典统计力学

The 1s electron cloud in hydrogen atom has the largest probability density distribution around a spherical shell with Bohr radius a 0. The author thinks the probability density distribution and electron cloud belong in fact,to statistic regularity, and imply a macro-time scale is used, therefore in hydrogen molecule the product of energy and time is far larger than Planck Constant.

氢原子中 1s电子的电子云呈球形，电子的最大几率密度分布出现在玻尔半径a0 的球壳内，认为几率密度分布及电子云属统计规律，意味着已经使用了宏观时标，这样就使氢分子体系中能量和时间的作用量远大于普郎克常数；根据电子云的交叠，用经典力学计算了基态氢分子的结构常数，获得键长、键能及力常数的表达式分别为Re=2a0 ，De=ze/4 2a0 ，k=ze/2 2a30 ，采用原子单位 a 。u 。

This book analyzes, from a single perspective, some of the most important applications: the critical-point theory in classical statistical mechanics, the scalar quantum field theories in two and three space-time dimensions, and Tomonaga's theory of the ground state of one-dimensional Fermi systems.

这本书分析，从一个单个的视角，一些最重要的应用：在经典统计力学方面的临界点理论，标量量领域理论在2 和3 空间时间维，和Tomonaga 一维费密系统的基态的理论方面。

By comparison between equations of motion of geometrical opticsand that of classical statistical mechanics,we find that there should be an analogy between GO and CSM instead of GO and classical mechanics.

本文将几何光学和经典统计力学的运动方程相比较之后，指出几何光学应与经典统计力学具有相似性，而不是与经典力学具有相似性。

Fundamental Principles of Quantum and Classical Statistical Mechanics - N-body Problem; Phase Space; Statistics and Distribution Functions and Averaging Methods; Boltzmann Distribution

量子基本原理与经典统计力学——N-body问题；相空间；统计学分布函数与平均方法；Boltzmann分布。

In theory, kinetic theory of gases with classical mechanics and statistical methods based on the thermal motion and interaction to make the appropriate simplifying assumptions, gives molecular modeling and collision mechanisms, using probability theory dealing with a large number of elements of collective behavior, characterized by the collective movement find the statistical average value.

理论上，气体动理论以经典力学和统计方法为基础，对热运动及相互作用做适当的简化假设，给出分子模型和碰撞机制，借助概率理论处理大量分子的集体行为，求出表征集体运动的统计平均值。

Postulates of classical statistical mechanics, micro canonical, canonical, and grand canonical distributions; applications to lattice vibrations, ideal gas, photon gas.

经典统计力学的假定、微正则、正则和巨正则分布；统计力学在晶格振动中的应用、理想气体、光子气体。

Geornetrical optics ; classical statistical mechanics ; quantum mechanics ; classical lirnit

几何光学；经典统计力学；量子力学；经典极限

Classical Statistical Mechanics; Hamiltonian and Ideal Gases; Factoring the Partition Function with the Semi-classical Approximation; PVTN Properties via Configuration Integral from Intermolecular Effects; Grand Canonical Ensemble I

经典统计力学；Hamilton函数与理想气体；半经典近似微分函数因数；对分子间作用，作定积分而得的PVTN性质；巨正则效果I。

This article consists of four parts: In the first part of thesis introduced Heisenberg's early years of life and the creation of Matrix mechanics, expounded Münich、G?ttingen,Copenhagen, three places different academic atmosphere which produce to Heisenberg's institute of physics, and revealed how to set up Matrix mechanics by mathematics method; The second part introduce Schr?dinger's university life, the research results, and the establishment of Wave mechanics. The different academic atmosphere of Vienna and Zürich have the difference influence which brings to Schr?dinger's research work, how to establishment the Schr?dinger equation based on Hamilton equation of classical mechanics, and elaborated the physical controversy caused by the equivalent.; The third part analyzed two mechanics different approaches in which the way to propose the question and solve the question; The last part recommend the different philosophy interpretations, Schr?dinger's interpretation onΨfunction, the statistical interpretation of Wave mechanics, uncertainty principle, and which caused this free discussion of quantum mechanics.

文章共分为四部分：第一部分介绍了海森伯的早年生活及其创立矩阵力学的过程，阐明了慕尼黑、哥廷根、哥本哈根三地不同的学术氛围对海森伯的物理研究所产生的不同作用，并揭示了海森伯如何用数学方法建立矩阵力学方程的过程；第二部分介绍了薛定谔的大学生活、研究成果，以及波动力学的创立过程，说明了维也纳和苏黎世不同的学术气氛给薛定谔的研究工作带来的不同影响，解释了薛定谔以经典哈密顿方程为基础建立薛定谔方程的过程，并阐述了等价性所引起的物理争论；第三部分分析了两种力学的思想进路在提出问题、解决问题上的不同；最后一部分介绍了对两种力学形式不同的哲学诠释，薛定谔对Ψ函数的诠释、波函数的统计解释和测不准原理，以及由此引起的量子力学的大讨论。

It is pointed out that the main tendency of this study is gradually turned from the traditional solution theory or semiempirical model to statistical mechanics theory , from primitive to nonprimitive electrolyte model, in o rder to estab lish the mo lecu lar thermodynam ic model at h igh level,which can predict them acroscopic thermodynamic properties of electrolyte solution system from the microscopic molecular and ionic parameters.

指出电解质溶液的研究已逐渐从经典的溶液理论和半经验模型转向用统计力学理论进行研究，从电解质的原始模型转向非原始模型。从分子和离子的微观参数出发建立高水平的热力学理论模型，以预测电解质溶液体系的宏观热力学性质，是发展的必然趋势。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新