波函数与波粒二象性

1、 波函数与波粒二象性 波函数与波粒二象性胡唐锦，深圳大学胡 良，深圳市宏源清实业有限公司 摘要，波函数是表达微观系统状态的函数。在经典力学中，可用质点的位置及动量表达宏观质点的状态。由于具有波粒二象性，位置及动量不能同时有确定值，因此，可用波函数表达系统的状态。声速是介质中微弱压强扰动的传播速度，其大小与介质的性质及状态有关。光速是指光子（电磁波）在真空中的传播速度（物理学常数）；光速是最大的信号速度（宇宙中），所有的物质的信号速度都不能够超过真空中的光速。力矢量与位移矢量之间有两种乘积，点乘及叉乘；点乘与做功有关，而叉乘与力矩有关。两个物体之间的作用总是相互的，物体之间相互作用的一对力，就称

2、为作用力及反作用力。有作用力就相应的有反作用力。显然，将其中任何一个力称为作用力，则另一个力就称为反作用力。关键词：波函数,波粒二象性,宏观物体，粒子，声速，光速，信号速度，力矩，功，能量，作用力，反作用力，能量，能量守恒，能量相互转化，量子场论，波函数，辐射，能量，万有引力，张量，位置，动量，万有引力，质量，距离，万有引力定律，万有引力定律拓展 作者：总工，高工，硕士，副董事长 ,23200514220引言波函数是表达微观系统状态的函数。在经典力学中，可用质点的位置及动量表达宏观质点的状态。由于具有波粒二象性，位置及动量不能同时有确定值，因此，可用波函数表达系统的状态。1电场及磁场介质在电场

3、（或磁场）的作用下，将被极化（或磁化），从而出现附加电荷及电流。这些附加的电荷及电流，也要激发电磁场，导致原来的宏观电磁场发生一些改变。对于极化（介质对电场的响应）来说，如果是导电介质（导体），存在大量的自由电子可在内部自由移动。如果是绝缘介质（电介质），电子被束缚在分子（或原子）范围内，不能够在宏观体积内自由移动。能量最低原理的内涵是指势能最低；从另一个角度来看，就是对周围的引力最大，因此，也可称为引力最大原理。物质为了保持稳定，就会自动降低其能量，来保持平衡。由于，能量最低的状态比较稳定，体现为能量最低原理。能量最低原理与最小作用量具有相似性。任何满足边界条件的连续函数x(t)就是路径；对

4、于每一条可能的路径x(t)，都可根据某个规则计算出相应的物理学量，可称为量子三维常数作用量（），即，。而最稳定的路径就是那条具有量子三维常数作用量（）的路径，即，能量最低原理。，其中，量子三维常数作用量，量纲，*L(3)T(-3)；，内禀空间，量纲，；，能量-动量张量，量纲，L(3)T(-3)；，能量，量纲，*L(2)T(-2)；，质量，量纲，；，路径，量纲，L(1)T(0)L(1)T(-1)L(0)T(1)L(1)T(-1）；0，真空电容率，量纲，；Xe，极化率，量纲，L(0)T(0）；E，电场强度，量纲，L(1)T(-2）L(3)T(-2）/L(2)T(0）L(1)T(-1);0， vac

5、uum permittivity, dimension, ;Xe， polarizability, dimension, L(0)T(0);E， electric field strength, dimension, L(1)T(-2)L(3)T(-2)/L(2)T (0)L(3)T(-2）L(1)T(-1）L(1)T(0）L(1)T(-1）L(3)T(-2)L(1)T(-1)L(1)T(0)L(1)T(-1)L(0)T(-1）L(0)T(-1）L(0)T(-1）L(1)T(-1）L(0)T(-1)L(0)T(-1)L(0)T(-1)L(1)T(-1)L(1)T(-1）L(1)T(-1）L(1

6、)T(-1）L(1)T(-1）L(3)T(-2）L(1)T(-1）L(1)T(-1)L(1)T(-1)L(1)T(-1)L(1)T(-1)L(3)T(-2)L(1)T(-1)L(1)T(-1）；0，真空电容率，量纲，；E，电场强度，量纲，L(1)T(-2）L(1)T(-1）L(3)T(-2）L(1)T(-1）L(-2)T(1）L(3)T(-2）L(1)T(-1);0， vacuum permittivity, dimension, ;E， electric field strength, dimension, L(1)T(-2)L(1)T(-1)L(3)T(-2)L(1)T(-1)L(-2)T

7、(1)L(3)T(-2)L(1)T(-1）L(0)T(-1）L(3)T(-2）L(1)T(-1）L(1)T(0）L(1)T(-1）L(1)T(-1)L(0)T(-1)L(3)T(-2)L(1)T(-1)L(1)T(0)L(1)T(-1)L(1)T(-1)L(0)T(-1)L(1)T(-1）L(3)T(-2)L(1)T(-1)L(1)T(-1）L(1)T(-1)L(0)T(-1)L(1)T(-1)L(3)T(-2)L(1)T(-1)L(1)T(-1).第二种情况，如果介质是运动的，并且吸收了光子；则有，The second case, if the medium is moving and ab

8、sorbs photons;Then there is, Ekn=Q* H=Q（jfC）+QpDt+QVPSp+nf；其中，Ekn,系统的总能量，量纲，*L(2)T(-2）；Q ，总电荷量（有效电荷总量），量纲，；H，辅助磁场（相当于电通量），量纲，L(3)T(-2）L(1)T(-1）L(1)T(0）L(1)T(-1）；in,Ekn, the total energy of the system, dimension, *L(2)T(-2);Q ，Total charge (total effective charge), dimension, ;H， auxiliary magnetic f

9、ield (equivalent to electric flux), dimension, L(3)T(-2)L(1)T(-1)L(1)T(0)L(1)T(-1)L(1)T(-1）L(1)T(-1）L(1)T(-1）L(0)T(0）；，光子的普朗克常数，量纲，*L(2)T(-2）L(0)T(-1）L(1)T(-1)L(1)T(-1)L(1)T(-1)L(0)T(0);， Plancks constant of photon, dimension, *L(2)T(-2)L(0)T(-1)-L(3)T(-1）L(3)T(-2）；(Vpfp)，表达电荷，量纲，；(C2p)，表达电荷相对应的电场（通

10、量），量纲，；(Vpfp)f，表达在导线中的相对磁荷，量纲，-L(3)T(-2）L(3)T(-1）-L(3)T(-1)L(3)T(-2);(Vpfp)， express charge, dimension, ;(C2p)， express the electric field (flux) corresponding to the charge, dimension, ;(Vpfp)f，the relative magnetic charge expressed in the wire, dimension, -L(3)T(-2)L(3)T(-1);(Vpfp)fp，表达磁荷，量纲，；Cp(2

11、，表达磁荷相对应的磁场（通量），量纲，。Ve，电子的空间荷，量纲，；Ve,电子内禀一维空间速度（信号速度），量纲，L(1)T(-1）L(0)T(-1）L(1)T(0）L(1)T(0）L(1)T(-1）。(Vpfp)fp，express magnetic charge, dimension, ;Cp(2， express the magnetic field (flux) corresponding to the magnetic charge, dimension, .Ve，the space charge of the electron, dimension, ;Ve， electron i

12、ntrinsic one-dimensional space velocity (signal velocity), dimension, L(1)T(-1)L(0)T(-1)L(1)T(0)L(1)T(0)L(1)T(-1)L(3)T(-1）L(1)T(-1）L(3)T(-1）/L(2)T(0）L(2)T(0）L(3)T(-1)L(1)T(-1)L(3)T(-1)/L(2)T (0) L(2)T(0)L(3)T(-2）L(1)T(-2）L(3)T(-2）/L(2)T(0）L(2)T(0）L(3)T(-2)L(1)T(-2)L(3)T(-2)/L(2)T (0) L(2)T(0)L(3)T(-

13、2）L(1)T(-2）L(3)T(-2）/L(2)T(0）L(2)T(0）；，负电荷单元（收敛属性），量纲，；，真空电容率，量纲，；，电荷数量（自由电荷及束缚电荷），量纲，L(0)T(0）；，普朗克频率，量纲，。in, electric flux (divergent property), L(3)T(-2)L(1)T(-2)L(3)T(-2)/L(2)T (0) L(2)T(0);, negative charge unit (convergence property), dimension, ;, vacuum permittivity, dimension, ;, the number

14、of charges (free charge and bound charge), dimension, L(0)T(0);, Planck frequency, dimension, .2电场及磁场的内涵对于电子来说，其表达式为：For electrons, the expression is: ；其中，表达一个负电荷（收敛属性），量子化，量纲，；，表达电通量（发散属性），量纲，L(3)T(-2）。in, express a negative charge (convergence property), quantization, dimension, ;, express electri

15、c flux (divergent property), dimension, L(3)T(-2).对于自旋的电子来说，其表达式为，For spin electrons, its expression is, ；其中，表达电子的磁荷（收敛属性），量子化，量纲，；，表达磁通量（发散属性），量纲，L(3)T(-1)。in, expressing the magnetic charge of the electron (convergent property), quantization, dimension, ;, expressing the magnetic flux (divergent p

16、roperty), dimension, L(3)T(-1).对于质子来说，其表达式为：For protons, the expression is:；其中，表达正电荷（收敛属性），量子化，量纲，；，表达电通量（发散属性），量纲，L(3)T(-2)。in, express positive charge (convergent property), quantization, dimension, ;, expressing electric flux (divergent property), dimension, L(3)T(-2).对于自旋的质子来说，其表达式为，For spin pro

17、tons, the expression is, ；其中，表达质子的磁荷（收敛属性），量纲，；，表达磁通量（发散属性），量纲，L(3)T(-1)。in, express the magnetic charge of proton (convergent property), dimension, ;, expressing the magnetic flux (divergent property), dimension, L(3)T(-1)L(3)T(-1)*L(1)T(-2)L(1)T(-1)L(1)T(0)；，普朗克频率,量纲，；，普朗克空间,量纲，.in, express magnet

18、ic force, dimension, L(3)T(-1)*L(1)T(-2)L(1)T(-1)L(1)T(0);, Planck frequency, dimension, ;， Planck space, dimension, .3麦克斯韦方程的内涵麦克斯韦方程表达了电场，磁场，电荷密度及电流密度等之间联系的偏微分方程；其由四个方程组成：第一，表达电荷如何产生电场的高斯定律；第二，高斯磁定律；第三，表达时变磁场如何产生电场的法拉第感应定律；第四，表达电流及时变电场如何产生磁场的麦克斯韦-安培定律。3 The meaning of Maxwells equationsMaxwells eq

19、uations express the partial differential equations of the connection between electric field, magnetic field, charge density, and current density; it consists of four equations: first, Gausss law, which expresses how electric fields are generated by electric charges; second, Gausss law of magnetism;

20、third , Faradays law of induction, which expresses how a time-varying magnetic field produces an electric field; fourth, Maxwell-Amperes law, which expresses how a current and a time-varying electric field produce a magnetic field.麦克斯韦方程组乃是由四个方程共同组成的：第一，高斯定律，该定律体现了电场与空间中电荷分布的关系；电场线始于正电荷，终止于负电荷。可通过计算

21、穿过某给定闭曲面的电场线数量（电通量），可知道包含在该闭曲面内的总电荷。更详细地说，该定律表达了穿过任意闭曲面的电通量与该闭曲面内的电荷之间的联系。Maxwells equations are composed of four equations:First, Gausss law,This law expresses the relationship between the electric field and the distribution of electric charges in space; electric field lines start with positive cha

22、rges and end with negative charges.The total charge contained within a given closed surface can be known by counting the number of electric field lines (electric flux) passing through that closed surface. In more detail, the law expresses the connection between the electric flux through any closed s

23、urface and the charge within that closed surface.高斯定律可表达为：Gausss law can be expressed as: ；其中，电场强度，量纲，L(1)T(-2)L(2)T(0)；，电荷（收敛属性），量纲，；，真空介电常数，量纲，；，闭合曲面所包围的体积，量纲，L(3)T(0)L(1)T(-2)L(2)T(0);, charge (convergence property), dimension, ;, vacuum permittivity, dimension, ;, the volume enclosed by the clos

24、ed surface, dimension, L(3)T(0)L(0)T(-1)L(3)T(-1)/L(3)T(0)L(0)T(-1)L(3)T(-1)/L(3)T(0) L(3)T(-2)L(3)T(-2).这意味着，穿过一个任意的封闭曲面的电场通量正比于其内部的电荷量；电场通量（场属性）从电荷（粒子属性）出发后，不可能凭空消失，也不可能凭空产生。也就是说，电荷（粒子属性）与相应的电场通量（场属性）构成了一个整体物质（例如，电子）。显然，该方程的左边，体现为场属性；该方程的右边，体现了荷属性。此外，假设，不存在电荷的源头（无源场），则进入封闭曲面内的电通量（）等于离开封闭曲面内的电通量（）。

25、值得注意是，具有正电属性的基本粒子（含有正电荷）是基本粒子；具有负电属性的基本粒子（含有负电荷）也是基本粒子，可独立存在。值得一提的是，根据量子三维常数理论，对于电子来说，其表达式为：It is worth mentioning that, according to the quantum three-dimensional constant theory,For electrons, its expression is: ；其中，表达一个负电荷，量子化的，量纲，；，表达电通量（发散属性），量纲，L(3)T(-2)。in, express a negative charge, quantize

26、d, dimension, ;, expressing electric flux (divergent property), dimension, L(3)T(-2).假设有N个电子包含在闭曲面内，则有，第一种情况，总电荷是，量纲，；相对应的穿过某给定闭曲面的电场线数量（电通量）是，NC2*p，量纲，L(3)T(-2)。Assuming that there are N electrons contained in the closed surface, there are,In the first case,The total charge is, , dimension, ;The co

27、rresponding number of electric field lines (electric flux) passing through a given closed surface is,NC2*p, dimension, L(3)T(-2)L(3)T(-2)L(3)T(-2).换句话说，磁荷（），收敛属性,量纲，。电通量（），发散属性,量纲，L(3)T(-2)。In other words, magnetic charge (), convergence property, dimension, .Electric flux (), divergence property, d

28、imension, L(3)T(-2)L(1)T(-1)L(3)T(-1)/L(2)T(0)L(2)T(0)L(3)T(-1)L(1)T(-1)L(3)T(-1)/L(2)T (0) L(2)T(0)L(3)T(-1)L(1)T(-1)L(1)T(-1)L(1)T(-1)L(1)T(-1)L(1)T(-1)L(1)T(-1)L(1)T(-2)L(3)T(-2)/L(2)T(0)；，普朗克长度，量纲，；，闭合曲线，量纲，L(1)T(0)L(3)T(-1)L(2)T(0)L(1)T(-1)L(3)T(-1)/L(2)T(0)L(0)T(1)L(1)T(-2)L(3)T(-2)/L(2)T(0) ;

29、, Planck length, dimension, ;, closed curve, dimension, L(1)T(0)L(3)T(-1)L(2)T(0)L(1)T(-1)L(3)T(-1)/L(2)T(0) L(0)T(1)L(3)T(-2)L(3)T(-2)L(1)T(-1)L(3)T(-1)/L(2)T(0)；，普朗克长度，量纲，；，闭合曲线，量纲，L(1)T(0)L(1)T(-1)L(2)T(0)L(1)T(-1)；，真空介电常数，量纲，；，普朗克时间，量纲，。in, the magnetic field strength,Dimensions, L(1)T(-1)L(3)T(

30、-1)/L(2)T(0) ;, Planck length, dimension, ;, closed curve, dimension, L(1)T(0)L(1)T(-1)L(2)T(0)L(1)T(-1);, vacuum permittivity, dimension, ;, Planck time, dimension, .该公式右边，第一项，揭示了，电流（I ）可以产生磁场（例如，通电的线圈相当于一个磁铁）。第二项，揭示了，感应磁场在空间环路上的积累正比于电场通量的变化速度。总之，该方程体现了磁通量（）具有守恒性，量纲，L(3)T(-1)L(3)T(-1)L(3)T(-1)。电荷（，

31、收敛属性）,量纲，；磁通量（，发散属性）,量纲，L(3)T(-1)L(3)T(-1)L(3)T(-1).charge (), convergence property , dimension, ;Magnetic flux (), divergence property , dimension, L(3)T(-1)L(1)T(-1)L(3)T(-1)/L(2)T(0)L(2)T(0)L(3)T(-1)L(1)T(-1)L(3)T(-1)/L(2)T (0) L(2)T(0)L(3)T(-1)L(0)T(-1)L(3)T(-1)/L(3)T(0)。，真空介电常数，量纲，；，普朗克长度，量纲，；t

32、,时间，量纲，L(0)T(1)；0,真空磁导率，量纲，；，真空介电常数，量纲，；J,传导电流，量纲，L(1)T(-1)L(1)T(-2)L(3)T(-2)/L(2)T(0)L(1)T(-1)L(3)T(-1)/L(2)T(0)L(1)T(-1)L(1)T(-1)L(1)T(0)L(1)T(-1)；0,真空磁导率，量纲，；0，真空介电常数，量纲，；S，曲面面积，量纲，L(2)T(0)L(1)T(-2)L(3)T(-2)/L(2)T(0)L(1)T(-1)L(1)T(-1)L(0)T(-1)-L(3)T(-1)/L(3)T(0)L(1)T(-1)L(0)T(-1)-L(3)T(-1)/L(3)T(

33、0) L(1)T(-1)L(2)T(0)L(2)T(0)；Qf，在闭合曲面（S）里面的自由电荷，量纲，。in,D, electric displacement, dimension, L(1)T(-1)L(2)T(0)L(2)T(0);Qf, free charge inside the closed surface ( ), dimension, .二，高斯磁定律微分表达式，Second, Gausss law of magnetismdifferential expression, B=0；其中，B，磁场强度，量纲，L(1)T(-1)L(1)T(-1)L(2)T(0)L(2)T(0)L(1

34、)T(-1)L(2)T(0)L(2)T(0)L(1)T(-1)L(1)T(-2)L(1)T(-1)；p，普朗克长度，量纲，；t，时间，量纲，L(0)T(1L(1)T(-2)L(1)T(-1);p, Planck length, dimension, ;t, time, dimension, L(0)T(1L(1)T(-2)L(1)T(0)L(1)T(0)；p，普朗克长度，量纲，；B,穿过闭合路径所包围的曲面（S）的磁通量，量纲，L(3)T(-1)L(0)T(1)L(1)T(-2)L(1)T(0)L(1)T(0);p, Planck length, dimension, ;B, the magn

35、etic flux passing through the surface (S ) enclosed by the closed path, dimension, L(3)T(-1)L(0)T(1)L(3)T(-2)-L(3)T(-1)/L(2)T(0)L(1)T(-1)；p,普朗克长度，量纲，；t，时间，量纲，L(0)T(1）L(3)T(-2)-L(3)T(-1)/L(2)T(0), or, L(1)T(-1) ;0, vacuum permeability, dimension, ;D, electric displacement, dimension, L(1)T(-1);p, Pla

36、nck length, dimension, ;t, time, dimension, L(0)T(1)L(3)T(-2)L(1)T(0)L(1)T(0)L(1)T(-1)L(3)T(-1)L(0)T(1）L(3)T(-2)L(1)T(0)L(1)T(0)L(1)T(-1)L(3)T(-1)L(0)T(1)L(1)T(-2)L(0)T(-1)L(3)T(-1)/L(3)T(0)；0=tp，真空电容率，量纲， ;tp,普朗克时间，量纲， 。in,E, electric field strength, dimension, L(1)T(-2)L(0)T(-1)L(3)T(-1)/L(3)T(0)

37、;0=tp, vacuum permittivity, dimension, ；tp, Planck time, dimension, 。积分表达式，Integral expression, SEda = Q0 ；其中，E，电场强度，量纲，L(1)T(-2)L(2)T(0)L(2)T(0)；Q，在闭合曲面（S）里面的总电荷，量纲，；0=tp，真空电容率，量纲， ；tp，普朗克时间，量纲， 。in,E, electric field strength, dimension, L(1)T(-2)L(2)T(0)L(2)T(0);Q, the total charge in the closed s

38、urface (S), dimension, ;0=tp, vacuum permittivity, dimension, ;tp, Planck time, dimension, .二，高斯磁定律微分表达式，Second, Gausss law of magnetismDifferential Expressions, B=0；其中，B磁场强度，量纲，L(1)T(-1)L(1)T(-1)L(2)T(0)L(2)T(0)L(1)T(-1)L(2)T(0)L(2)T(0)L(1)T(-1)L(1)T(-2)L(1)T(-1)；p，普朗克长度，量纲，；t，时间，量纲，L(0)T(1L(1)T(-2

39、)L(1)T(-1);p, Planck length, dimension, ;t, time, dimension, L(0)T(1L(1)T(-2)L(1)T(0)L(1)T(0)；p，普朗克长度，量纲，；B,穿过闭合路径所包围的曲面（S）的磁通量，量纲，L(3)T(-1)L(0)T(1)L(1)T(-2)L(1)T(0)L(1)T(0);p, Planck length, dimension, ;B, the magnetic flux passing through the surface ( S) enclosed by the closed path, dimension, L(

40、3)T(-1)L(0)T(1)L(1)T(-1)L(3)T(-1)/L(3)T(0)L(0)T(-1)；0，真空磁导率，量纲，;0，真空电容率（真空介电常量），量纲，;，电场强度，量纲，L(1)T(-2)L(0)T(1)L(1)T(-1)L(3)T(-1)/L(3)T(0)L(0)T(-1) ;0, vacuum permeability, dimension, ;0, vacuum permittivity (vacuum dielectric constant), dimension, ;, electric field strength, dimension, L(1)T(-2)L(0)

41、T(1)L(1)T(-1)L(1)T(0)L(1)T(0)L(3)T(-2)；Q,在闭合曲面内的总电荷，量纲，;0,真空磁导率，量纲，;，穿过闭合路径所包围的曲面（S）的总电流，量纲，L(1)T(-1)L(0)T(1)L(1)T(-1)L(1)T(0)L(1)T(0)L(3)T(-2);Q, the total charge in the closed surface, dimension, ;0, vacuum permeability, dimension, ;, the total current passing through the surface ( ) enclosed by t

42、he closed path, dimension, L(1)T(-1)L(0)T(1)L(1)T(-1)；，电容率（介电常量），量纲，;，电场强度，量纲，L(1)T(-2)L(1)T(-1);, permittivity (dielectric constant), dimension, ;, electric field strength, dimension, L(1)T(-2)L(1)T(-1)；，磁导率，量纲，;H，辅助磁场（相当于电通量），量纲，L(3)T(-2)L(1)T(-1);, permeability, dimension, ;H, auxiliary magnetic

43、field (equivalent to electric flux), dimension, L(3)T(-2)L(3)T(-2)*L(1)T(0)L(1)T(-1)L(2)T(0)L(3)T(-2)*L(1)T(0)L(1)T(-1)L(2)T(0)L(3)T(-1)*L(1)T(-2)L(1)T(0)L(5)T(-3)L(3)T(-2)*L(1)T(0)L(1)T(-1)L(3)T(-1)*L(1)T(-2)*L(1)T(0)L(5)T(-3)L(3)T(-1)*L(1)T(-2)L(1)T(0)L(5)T(-3)L(3)T(-2)*L(1)T(0)L(1)T(-1)L(3)T(-1)*

44、L(1)T(-2)*L(1)T(0) L(5)T(-3).第二大类基本粒子（电子及质子等）因内禀自旋而产生磁矩;而，基本粒子（电子及质子等）的内禀磁矩的大小都是物理学常数。磁矩的方向取决于粒子的自旋方向，例如，如果电子磁矩的测量值是负值；这意味着电子的磁矩与内禀自旋呈现相反的方向。The second categoryElementary particles (electrons and protons, etc.) generate magnetic moments due to their intrinsic spin; however, the magnitudes of the int

45、rinsic magnetic moments of elementary particles (electrons, protons, etc.) are all physical constants.The direction of the magnetic moment depends on the spin direction of the particle, for example, if the measured value of the electrons magnetic moment is negative; this means that the electrons mag

46、netic moment is in the opposite direction to its intrinsic spin.电子可表达为：Electron can be expressed as: C2p =Cp(2)=(Cp)p=Cp=Ve Ve(3) =（Vefe )Ve(2)e = meVe(2)*e .显然，电子的内禀磁矩可表达为：Obviously, the intrinsic magnetic moment of the electron can be expressed as: =geBSi ;其中，=(Vpfp)fpp，电子的内禀磁矩，量纲，*L(1)T(0); ge,电子

47、的朗德因子，量纲，; Si=,电子内禀自旋，量纲，; ,普朗克常数，量纲，*L(2)T(-2); B=(eme),玻尔磁子，量纲，; e=(Vpfp)，电子的基本电荷，量纲，; me，电子的质量，量纲，。in,=(Vpfp)fpp, the intrinsic magnetic moment of the electron,Dimension, *L(1)T(0);ge, the electrons Lande factor, dimension, ;Si=, electron intrinsic spin, dimension, ;, Plancks constant, dimension,

48、 *L(2)T(-2);B=(eme), Bohr magneton, dimension, ;e=(Vpfp), the basic charge of the electron, dimension, ;me, the mass of the electron, dimension, .电阻及电流的内涵电阻（R）是表达导体导电性能的物理量。电阻（R）可由导体两端的电压（U）与通过该导体的电流（I）的比值来定义，可表达为，The meaning of resistance and currentResistance (R) is a physical quantity that expres

49、ses the electrical conductivity of a conductor. Resistance (R) can be defined by the ratio of the voltage across a conductor (U) to the current (I) through that conductor, and can be expressed as, R=U/I ;其中，R，电阻，量纲，;U，电压，量纲，*L(1)T(-2)L(1)T(-1)。in,R, resistance, dimension, ;U, voltage, dimension, *L(

50、1)T(-2)L(1)T(-1).电阻(R)大小可用来衡量导体对电流阻碍作用的强弱（导电性能的好坏）。而，电阻的倒数(1/R)称为电导()，是表达导体导电性能的物理量。电阻是揭示导体导电性能的参数;对于由某种材料制成的柱形均匀导体，其电阻（R）与长度（L）成正比，而与横截面积（S）成反比;可表达为：The resistance (R) can be used to measure the strength of the resistance of the conductor to the current (the quality of the electrical conductivity).

51、However, the reciprocal of resistance (1/R) is called conductance (), which is a physical quantity that expresses the conductivity of a conductor.Resistance (R) is a parameter that reveals the conductive properties of a conductor; for a cylindrical uniform conductor made of a certain material, its r

52、esistance (R) is proportional to its length (L) and inversely proportional to its cross-sectional area (S);It can be expressed as: R= LS ；其中，R,电阻，量纲，;，电阻率，量纲，;L，导电材料的长度，量纲，L(1)T(0)L(2)T(0);，电导，量纲，。in,R, resistance, dimension, ;, resistivity, dimension, ;L, the length of the conductive material, dime

53、nsion, L(1)T(0)L(2)T(0);, conductance, dimension, .值得一提的是，电阻率（）是由导体的材料及周围温度等所决定，可表达为：It is worth mentioning that the resistivity () is determined by the material of the conductor and the surrounding temperature, etc. It can be expressed as: =0（1+T）；其中，电阻率，量纲，;0，温度是0时的电阻率，量纲，;，为电阻的温度系数，量纲，;T，温度，量纲，L(

54、3)T(-2),或，*L(2)T(-2)L(3)T(0)。, resistivity, dimension, ;0, the temperature is the resistivity at 0, dimension, ;, is the temperature coefficient of resistance, dimension, ;T, temperature, dimension, L(3)T(-2),Or, *L(2)T(-2)L(3)T(0).值得注意的是，半导体与绝缘体的电阻率跟金属不同，它们与温度之间不是按线性规律变化的。当温度升高时，它们的电阻率会急剧地减小（体现出非线性

55、变化的性质）。It is worth noting that the resistivity of semiconductors and insulators, unlike metals, does not vary linearly with temperature. As the temperature increases, their resistivity decreases sharply (indicating a nonlinear change).电流的本质，导体中的自由电荷在电场力的作用下做有规则的定向运动可形成电流；而，正电荷定向流动的方向就是电流方向。the natur

56、e of current,Under the action of electric field force, the free charges in the conductor can make regular directional movements to form current; however, the direction of directional flow of positive charges is the current direction.电通量（E）是电场的通量，与穿过一个曲面的电场线的数目成正比，是表征电场分布情况的物理量。 电通量（E）与金属导体中电流（I）具有内在

57、的联系，其微观表达式为：Electric flux (E) is the flux of the electric field, which is proportional to the number of electric field lines passing through a curved surface, and is a physical quantity that characterizes the distribution of the electric field. The electric flux (E) is intrinsically related to the c

58、urrent (I) in the metal conductor, and its microscopic expression is: I=E/neS=E/S=E0；其中，I, 电流,量纲，；E，电通量，量纲，L(3)T(-2)L(-3)T(0);e, 电荷量（自由电荷量），量纲，;,电荷密度，量纲，L(0)T(-1);0, vacuum permeability, dimension, ;S, 导体横截面积，量纲，L(2)T(0)。in,I, current, dimension, ;E, electric flux, dimension, L(3)T(-2)L(-3)T(0);e, c

59、harge (free charge), dimension, ;0, vacuum permeability, dimension, ;S, conductor cross-sectional area, dimension, L(2)T(0)L(3)T(-2);Q，电荷，量纲，;t，时间，量纲，L(0)T(1)L(3)T(-2);Q, charge, dimension, ;t, time, dimension, L(0)T(1)L(1)T(-2)L(3)T(-2)L(2)T(0)L(1)T(-2)L(3)T(-2)L(2)T(0).值得一提的是，磁荷之间的力可表达为：It is wort

60、h mentioning that the force between the magnetic charges can be expressed as: Fqm=qm1 qm2r00=qm1 qm2rC;其中，Fqm，磁荷之间的力，量纲，*L(1)T(-1);qm1，第一个磁荷的大小，量纲，;qm2，第二个磁荷的大小，量纲，;r，两个磁荷之间距离，量纲，L(1)T(0);0，真空磁导率，量纲，;0，真空电容率，量纲，;C，最大的信号速度,量纲，L(1)T(-1)。in,Fqm, the force between magnetic charges, dimension, *L(1)T(-1)