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Đây là bộ sách tiếng anh về chuyên ngành vật lý gồm các lý thuyết căn bản và lý liên quan đến công nghệ nano ,công nghệ vật liệu ,công nghệ vi điện tử,vật lý bán dẫn. Bộ sách này thích hợp cho những ai đam mê theo đuổi ngành vật lý và muốn tìm hiểu thế giới vũ trụ và hoạt độn ra sao.
[...]... useful for a number of scattering and di usion problems 6] 61] The main conclusion of the treatment of this section is that the transmission of a combination of two stacks of layers is not the product of the transmission coe cients of the two separate stacks Paradoxically, Berry and Klein 8] showed in their analysis of \transparent mirrors" that for a large stacks of layers with random transmission... It happens often in mathematical physics that a nal expression is complex very often nal results look so messy it is di cult to understand them However, often we know that certain terms in an expression can assumed to be very small (or very large) This may allow us to obtain an approximate expression that is of a simpler form In this way we trade accuracy for simplicity and understanding In practice,... critical value called the radius of convergence Details on the criteria for the convergence of series can be found for example in Boas?? or Butkov?? The second reason why the derivatives at one point do not necessarily constrain the function everywhere is that a function may change its character over the range of parameter values that is of interest As an example let us return to a moving particle and... direction of the 22 CHAPTER 3 SPHERICAL AND CYLINDRICAL COORDINATES basis vector change as well This is a di erent way of saying that the spherical coordinate system is not an inertial system When computing the acceleration in such a system additional terms appear that account for the fact that the coordinate system is not an inertial system The results of the section (3.1) contains all the ingredients... of a sphere with radius R using spherical coordinates Pay special attention to the range of integration for the angles and ', see section (3.1) 3.5 Cylinder coordinates Cylinder coordinates are useful in problems that exhibit cylinder symmetry rather than spherical symmetry An example is the generation of water waves when a stone is thrown in a pond, or more importantly when an earthquake excites a. .. the total transmission coe cients is the product of the transmission coe cients of the individual layers, despite the fact that multiple re ections play a crucial role in this process Chapter 3 Spherical and cylindrical coordinates Many problems in mathematical physics exhibit a spherical or cylindrical symmetry For example, the gravity eld of the Earth is to rst order spherically symmetric Waves excited... (3.1) a Cartesian coordinate system with its x, y and z -axes is shown as well as the location of a point r This point can either be described by its x, y and z -components or by the radius r and the angles and ' shown in gure (3.1) In the latter case one uses spherical coordinates Comparing the angles and ' with the geographical coordinates that de ne a point on the globe one sees that ' can be compared... C B u A = @ cos cos ' cos sin ' sin A @ uy A @ u' ; sin ' cos ' ; 0 uz (3.19) 3.3 The acceleration in spherical coordinates You may wonder whether we really need all these transformation rules between a Cartesian coordinate system and a system of spherical coordinates The answer is yes! An important example can be found in meteorology where air moves along a sphere The velocity v of the air can be... ection and transmission coe cient of a very thin layer using the Born approximation Let the re ection and transmission coe cient of a single thin layer n be denoted by rn respectively tn and let the re ection and transmission coe cient of a stack of n layers be denoted by Rn and Tn respectively Suppose the left stack consists on n layers and that we want to add an (n + 1)-th layer to the stack In that case... some applications one wants to integrate over the surface of a sphere rather than integrating over a volume For example, if one wants to compute the cooling of the Earth, one needs to integrate the heat ow over the Earth's surface The treatment used for deriving the volume integral in spherical coordinates can also be used to derive the surface integral A key element in the analysis is that the surface . (d) velocity variable acceleration acceleration