由刘维尔方程推导玻尔兹曼方程

刘维尔方程是统计物理中基本方程，因而原则上统计物理中许多重要方程都可以由刘维尔方程导出，本文尝试由刘维尔方程推导玻尔兹曼方程．     

从Schroedinger方程引申到Dirac方程的一种简单方法

从Schroedinger方程出发，结合自旋的唯象描述、简单的相对论考虑和适当的猜测，写出了Dirac方程的正确形式     

拉氏方程,阿贝尔方程的张量推导

本文应用线性代数、张量分析的基本概念说明拉氏方程、阿贝尔方程可以看作是牛顿方程在约束所允许的矢量空间中的协变分量形式，从而在不直接引用虚位移原理的前提下，导出这两个分析力学的基本方程．     

Manning-Rosen标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态

给出了具有Manning-Rosen型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态解，其解可用超几何函数表示. 关键词： Manning-Rosen势 Klein-Gordon方程 Dirac方程 束缚态     

异丁烷的饱和蒸汽压方程及饱和液体密度方程研究

1引言臭氧层正以惊人的速度被破坏，但在世界范围内CFC和HCFC用于制冷系统尤其是冰箱的量仍然很高，为了保护环境，迫切需要寻找新的更好的制冷剂。人们在寻找新的性能优良而又无公害制冷剂的过程中，意识到了碳氢化合物的价值。联合国环境规划署制冷技术评估小组称其为“长期的、经得起考验的制冷剂’巾］。本文对其中的异丁烷进行了研究，在分析比较的基础上，给出了异丁烷的新饱和蒸汽压方程和炮和液体密度方程，为进一步研究异丁烷的统一热物性方程提供了条件。2异丁烷的饱和蒸汽压方程2．1常用饱和蒸汽压方程的比较分析表1列出了常…     

几个典型的数学物理方程的物理解读

拉普拉斯方程、 泊松方程、 热传导方程( 扩散方程)和波动方程是大学物理教学中常见的几个典型的微 分方程, 分别涉及到了流体力学、 电磁学、 热学和波动等重点教学内容. 探索了如何用直观明确而容易理解的物理 语言解读这些方程. 从拉普拉斯方程的物理本质出发, 通过改变该方程右端的形式, 分别引出泊松方程、 热传导方 程( 扩散方程)和波动方程, 详细阐述了上述方程与相关物理现象之间的内在联系, 提出了一种关于以上方程的纵 向对比讲授法, 为学生深入理解典型的数学物理微分方程的物理含义提供了可行的思路     

一类广义Boussinesq方程和Boussinesq-Burgers方程新的显式精确解

利用一种推广的代数方法，求解了一类广义Boussinesq方程(B(m，n)方程)和Boussinesq-Burgers方程(B-B方程).获得了其多种形式的显式精确解，包括孤波解、三角函数解、有理函数解、Jacobi椭圆函数周期解和Weierstrass椭圆函数周期解，进一步丰富了这两类方程的解. 关键词： Boussinesq方程 Boussinesq-Burgers方程 推广的代数方法 显式精确解     

有关昂氏气态方程的几点讨论

本文叙述了有关昂氏气态方程（昂内斯气态方程的简称）的几点讨论。一是昂氏气态方程收缩为范式气态方程的讨论;二是昂氏气态方程温度昂T 和理想气态方程温度T理相等的压强（下面简称等温压强）的讨论;三是昂氏气态方程压强昂P 和理想气态方程压强P理相等的温度（下面简称等压温度）的讨论。     

有关昂氏气态方程的几点讨论

本文叙述了有关昂氏气态方程(昂内斯气态方程的简称)的几点讨论.一是昂氏气态方程收缩为范式气态方程的讨论;二是昂氏气态方程温度T昂和理想气态方程温度T理相等的压强(下面简称等温压强)的讨论;三是昂氏气态方程压强P昂和理想气态方程压强P理相等的温度(下面简称等压温度)的讨论.     

超导体流体动力学方程

本文从超导体中准粒子和声子的动力学方程及序参量方程出发得到了超导体流体动力学方程,从理论上证明了出现准粒子从浓度小的区域向浓度大的区域反常扩散的可能性以及对于短波涨落的稳定项。 关键词：     

整数自旋粒子的方程和波函数

从高自旋态的Bargmann-Wigner方程出发,建立了整数自旋粒子的运动方程,通过求解方程得到了一套整数自旋粒子波函数,并建立了等效Largrange形式.     

Dirac equation for the Hulthén potential within the Yukawa-type tensor interaction

Using the Nikiforov-Uvarov (NU) method, pseudospin and spin symmetric solutions of the Dirac equation for the scalar and vector Hulthén potentials with the Yukawa-type tensor potential are obtained for an arbitrary spin-orbit coupling quantum number κ. We deduce the energy eigenvalue equations and corresponding upper- and lower-spinor wave functions in both the pseudospin and spin symmetry cases. Numerical results of the energy eigenvalue equations and the upper- and lower-spinor wave functions are presented to show the effects of the external potential and particle mass parameters as well as pseudospin and spin symmetric constants on the bound-state energies and wave functions in the absence and presence of the tensor interaction.     

Conformal invariant two and three-point functions for fields with arbitrary spin

The conformal invariant two and three-point functions for any “fundamental” fields with an arbitrary spin and scale dimensions are found in the Minkowsky x-space. The two-point functions for Dirac, symmetric and antisymmetric tensor fields are given. The three-point functions for two Dirac fields and one symmetrical tensor field, as well as any other field for which this function is nonvanishing, are given. In the case of conserved currents the Ward identities are considered.     

Relativistic symmetry of position-dependent mass particle in Coulomb field including tensor interaction

The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction under the spin and pseudospin symmetric limit. Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ. Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit in the absence of tensor interaction.     

Lagrangian dynamics of polarized media with internal spin in general relativity

The complete system of field equations for a polarized medium with internal spin in interaction with an arbitrary set of fields is derived from a four-dimensional action integral. The general results are then specialized to the interaction with an Einstein-Maxwell field. The application to ideal spinning fluids is discussed.     

Averaging out the Einstein equations

A general scheme to average out an arbitrary 4-dimensional Riemannian space and to construct the geometry of the averaged space is proposed. It is shown that the averaged manifold has a metric and two equi-affine symmetric connections. The geometry of the space is characterized by the tensors of Riemannian and non-Riemannian curvatures, an affine deformation tensor being the result of non-metricity of one of the connections. To average out the differential Bianchi identities, correlation 2-form, 3-form and 4-form are introduced and the differential relations on these correlations tensors are derived, the relations being integrable on an arbitrary averaged manifold. Upon assuming a splitting rule for the average of the product including a covariantly constant tensor, an averaging out of the Einstein equations has been carried out which brings additional terms with the correlation tensors into them. As shown by averaging out the contracted Bianchi identities, the equations of motion for the averaged energy-momentum tensor do also include the geometric correction terms. Considering the gravitational induction tensor to be the Riemannian curvature tensor (then the non-Riemannian one is the macroscopic gravitational field), a theorem that relates the algebraic structure of the averaged microscopic metric with that of the induction tensor is proved. Due to the theorem the same field operator as in the Einstein equations is manifestly extracted from the averaged ones. Physical interpretation and application of the relations and equations obtained to treat macroscopic gravity are discussed.     

Symmetric hyperbolic systems for a large class of fields in arbitrary dimension

Symmetric hyperbolic systems of equations are explicitly constructed for a general class of tensor fields by considering their structure as r-fold forms. The hyperbolizations depend on 2r−1 arbitrary timelike vectors. The importance of the so-called “superenergy” tensors, which provide the necessary symmetric positive matrices, is emphasized and made explicit. Thereby, a unified treatment of many physical systems is achieved, as well as of the sometimes called “higher order” systems. The characteristics of these symmetric hyperbolic systems are always physical, and directly related to the null directions of the superenergy tensor, which are in particular principal null directions of the tensor field solutions. Generic energy estimates and inequalities are presented too. Examples are included, in particular a mixed gravitational-scalar field system at the level of the Bianchi equations.     

Vacuum Non Singular Black Hole Solutions in Tetrad Theory of Gravitation

Starting from a spherically symmetric tetrad with three unknown functions of the radial coordinate and assuming a specific form of the vacuum stress-energy momentum tensor, a general solution of Møller's field equations in case of spherically symmetric nonsingular black holes is derived. The general solution is characterized by an arbitrary function and two constants of integration. The previously obtained solutions are verified as special cases of the general solution. The associated metric of the general solution gives no more than the spherically symmetric nonsingular black hole obtained before. The energy content of the general solution depends on the asymptotic behavior of the arbitrary function, and is different from the standard one.