惯性参照系之间的时空变换及其唯一性问题

在狭义相对论的框架下,论述了在时空间隔保持不变的条件下,两个作相对运动的惯性参照系之间的时空变换一定是唯一的,而且这个唯一的变换就是洛伦兹变换。如果不考虑惯性参照系之坐标轴的平移与转动自由度问题,由时空间隔保持不变这一条件就直接得到了通常形式的洛伦兹变换。     

时空间隔在所有的惯性系中保持不变与洛伦兹变换

在狭义相对论的框架下,文中首先论述了在时空间隔保持不变的条件下,惯性系之间的时空变换一定是线性的,随后证明了在这一条件下惯性系之间的时空变换必定也是唯一的,最后证明了这唯一的时空变换就是洛伦兹变换.因此从时空间隔保持不变这一条件出发完全可以建立洛伦兹变换,文中在最后一节还论证了这一建立洛伦兹变换的条件是最基本的条件,没有其他更低的条件.     

洛伦兹变换成立的充分与必要条件

文中论述了两个作相对匀速运动的惯性参照系之间的时空变换是洛伦兹变换的充分与必要条件,这个条件就是时空间隔保持不变.     

狭义相对论中事件概念的教学

论述了事件概念的含义及准确理解事件在洛伦兹变换和相对论时空理论（运动时钟延缓、运动尺寸缩短等）教学中的作用．     

洛伦兹变换的引入及其时空图像讨论

狭义相对论是理工科大学物理课程教学中的一个难点,这是因为狭义相对论所涉及的时空效应在实际中都很难被观测到,而反映相对论时空观的洛伦兹变换又较为抽象,学生在学习过程中通常是机械地记忆公式,而并没有真正理解相对论的时空观及其与洛伦兹变换之间的联系.针对这一问题,本文介绍了一种引入洛伦兹变换的新方式:首先通过直观的思想实验定量地导出时间延缓、长度收缩和同时性的相对性等时空效应的数学表达式,然后在此基础上推导得到洛伦兹变换的x坐标变换式和时间变换式,并结合推导过程对其时空图像进行讨论.通过洛伦兹变换的这种引入方式可将相对论时空效应与洛伦兹变换紧密地联系起来,突出了洛伦兹变换的物理图像,从而加深学生对洛伦兹变换及相对论时空观的理解.     

关于洛伦兹变换的推导

介绍了从时空的一些普遍性质出发而推导洛伦兹变换的几种有代表性的方法，特别阐明了每种方法的推导依据（包括隐含的依据），并对这些依据所对应的物理意义进行了讨论。     

几何理解洛伦兹变换的时空内涵

洛伦兹变换是狭义相对论的核心内容.理解并掌握其内含的时空变换规律,对进一步理解狭义相对论时空观具有十分重要意义.本文基于时空图的二维旋转变换,从几何上对洛伦兹变换中所包含的"钟慢尺缩"时空变换本质和光速不变性等条件进行解析.使学生能够更加直观去感受并理解洛伦兹变换,为后续课程学习打下基础.     

为什么说狭义相对论是近代物理学的一大支柱

本文首先简要介绍了狭义相对论的两条基本假设:狭义相对性原理和光速不变原理。进而由光速不变原理定义了惯性系的时间坐标并连同相对性原理推导出洛伦兹变换。随后把相对性原理具体表述为:一切物理定律的方程式在洛伦兹变换下保持形式不变。最后着重说明了为什么说狭义相对论而非广义相对论是近代物理学(包括广义相对论)的一大支柱:所有平直时空的物理学理论其动力学方程式都在洛伦兹变换下保持形式不变;广义相对论是在弯曲时空的局部保持洛伦兹不变性。     

准洛伦兹变换与平面电磁波方程——多普勒效应

根据光速不变性和相对性原理,导出一对共轭变换．通过“比例中值定理”完成电磁场的洛伦兹变换．阐述了动系中平面电磁波方程和能流矢量共轭变换的形式．应用“相位不变性”原理讨论了多普勒效应光频的共轭变换,并借助于中值定理完成光频的洛伦兹变换．最后,引入爱因斯坦阐明的极隧射线实验来检验光频共轭变换及其推论的正确与否．     

为什么时空变换必须是线性的

尽管线性时空变换是狭义相对论的出发点,但至少从教学角度,对线性变换合理性的论证依然不清晰。笔者根据时空均匀性、时空各向同性和惯性系的等价性,严格地导出了时空的线性变换,其中关键概念是变换的时间缩放系数和空间缩放系数。沿此思路,进一步约束两个坐标系之间的时空缩放系数相等,并利用光速不变原理,导出了洛伦兹变换。     

Conformal invariance and conserved quantities of general holonomic systems in phase space

This paper studies the conformal invariance and conserved quantities of general holonomic systems in phase space. The definition and the determining equation of conformal invariance for general holonomic systems in phase space are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal single-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.     

相空间中变质量力学系统的Hojman守恒量

研究一般的无限小变换下相空间中变质量力学系统Lie对称性的Hojman守恒量. 给出了相空 间中变质量力学系统Lie 对称性的确定方程和Hojman守恒量定理,并举例说明结果的应用. 关键词： 相空间 变质量系统 一般的无限小变换 Lie对称性 Hojman守恒量     

Canonical transformations and exact invariants for time‐dependent Hamiltonian systems

An exact invariant is derived for n‐degree‐of‐freedom non‐relativistic Hamiltonian systems with general time‐dependent potentials. To work out the invariant, an infinitesimalcanonical transformation is performed in the framework of the extended phase‐space. We apply this approach to derive the invariant for a specific class of Hamiltonian systems. For the considered class of Hamiltonian systems, the invariant is obtained equivalently performing in the extended phase‐space a finitecanonical transformation of the initially time‐dependent Hamiltonian to a time‐independent one. It is furthermore shown that the invariant can be expressed as an integral of an energy balance equation. The invariant itself contains a time‐dependent auxiliary function ξ (t) that represents a solution of a linear third‐order differential equation, referred to as the auxiliary equation. The coefficients of the auxiliary equation depend in general on the explicitly known configuration space trajectory defined by the system's time evolution. This complexity of the auxiliary equation reflects the generally involved phase‐space symmetry associated with the conserved quantity of a time‐dependent non‐linear Hamiltonian system. Our results are applied to three examples of time‐dependent damped and undamped oscillators. The known invariants for time‐dependent and time‐independent harmonic oscillators are shown to follow directly from our generalized formulation.     

A unified symmetry of nonholonomic mechanical systems in phase space

In this paper, we have studied the unified symmetry of a nonholonomic mechanical system in phase space. The definition and the criterion of a unified symmetry of the nonholonomic mechanical system in phase space are given under general infinitesimal transformations of groups in which time is variable. The Noether conserved quantity, the generalized Hojman conserved quantity and the Mei conserved quantity are obtained from the unified symmetry. An example is given to illustrate the application of the results.     

高维增广相空间中广义力学系统的对称性和不变量

依据广义增广相空间中的Hamilton作用量在无穷小变换群作用下的不变性,给出广义完整保守和非保守力学系统的对称性和不变量及有关结论的逆命题,最后举一实例说明 关键词： 增广相空间 广义力学 对称性 不变量     

New non-Noether conserved quantities of mechanical system in phase space

This paper focuses on studying non-Noether conserved quantities of Lie symmetry and of form invariance for a mechanical system in phase space under the general infinitesimal transformation of groups. We obtain a new non-Noether conserved quantity of Lie symmetry of the system, and Hojman and Mei's results are of special cases of our conclusion. We find a condition under which the form invariance of the system will lead to a Lie symmetry, and, further, obtain a new non-Noether conserved quantity of form invariance of the system. An example is given finally to illustrate these results.     

Unified Symmetry of Nonholonomic System of Non-Chetaev＇s Type with Variable Mass in Event Space

The unified symmetry of a nonholonomic system of non-Chetaev＇s type with variable mass in event space is studied. The differential equations of motion of the system are given. Then the definition and the criterion of the unified symmetry for the system are obtained. Finally, the Noether conserved quantity, the Hojman conserved quantity, and a new type of conserved quantity are deduced from the unified symmetry of the nonholonomic system of non-Chetaev＇s type with variable mass in event space at one time. An example is given to illustrate the application of the results.     

Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space

This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.     

Hojman conserved quantity for nonholonomic systems of unilateral non-Chetaev type in the event space

Hojman conserved quantities deduced from the special Lie symmetry, the Noether symmetry and the form invariance for a nonholonomic system of the unilateral non-Chetaev type in the event space are investigated. The differential equations of motion of the system above are established. The criteria of the Lie symmetry, the Noether symmetry and the form invariance are given and the relations between them are obtained. The Hojman conserved quantities are gained by which the Hojman theorem is extended and applied to the nonholonomic system of the unilateral non-Chetaev type in the event space. An example is given to illustrate the application of the results.     

选择照射下核自旋波函数的变换特性

本文采取适用于一般多量子跃迁过程的讨论方法,当任意自旋的核处于恒定磁场和静电场中并受到单频或多频选择照射的条件下,对单个核的任意数目的相邻的子能级系统,其几率振幅的变换特性作一普遍分析,同时还讨论了上述变换特性的物理含义,阐明了粒子在空间旋转变换下波函数的2π或4π对称性,以及粒子在选择照射下子能级系统的几率振幅的2π或4π周期性的区别。 关键词：