刁勇强34-35-A17.doc

CHAPTER 2 Theory of SolidsThis value of energy may be given in the more common unit of electron-volts(see Appendix D).The electron-volt(ev) is the unit of energy equal to 1.610-19J.We can then write n CommentThe reciprocal relation between photon energy and wavelength is demonstrated:a large energy corresponds to a short wavelength. Exercise Problem EX2.1 Determine the energy(in eV)of a photon having wavelengths of(a) and (b). 2.1.2 wave- particle Duality principleWe have seen in the previous paragraphs that light waves,in the photoelectric effect,behave as if they are particles.In 1924,de Broglie postulated the existence of matter waves.He suggested that since waves exhibit particle-like behavior, then particles should be expected to show wave-like properties. The hypothesis of de Broglie is the existence of a wave-particle duality principle.The momentum of a photon is given by (2.2)Where is the wavelength of the light wave. Then,de Broglie hypothesized that the wavelength of a particle can be expressed as (2.3)Where p is the momentum of the particle and is known as the de Broglie wavelength of the matter wave.EXAMPLE 2.2OBJECTIVEDetermine the de Broglie wavelength of a particle. Consider an electron traveling at a velocity of 107cm/s=105m/s.n SolutionThe momentum is given by P = mv =(9.1110-31)(105)=9.1110-26Kg-m/sThen the de Briglie wavelength is 2.1 Principles of Quantum Mechanics or n CommentThis calculation shows the order of magnitude of the de Broglie wavelength for a “typical”electron. Exercise Problem EX2.2(a) Find the momentum and energy of a particle with mass 510-31Kg and a de Broglie wavelength of .(b)An electron has a kinetic energy of 20 meV.Derermine the de Broglie wavelength. To gain some appreciation of the frequencies and wavelengths involved in the wave-particle duality principle,Figure2.2 shows the electromagnetic frequency spectrum. We see that a wavelength of obtained in Example 2.2 is in the ultraviolet range.Typically,we will be considering wavelengths in the ultraviolet and visible range.These wavelengths are very short compared with the usual radio spectrum range. In some cases,electromagnetic waves behave as if are particles(photons)and,in some cases,particles behave as if they are waves,This wave-particle duality principle of quantum mechanics applies primarily to small particles such as electrons,but it has also been shown to apply to protons and neutrons.For very large particles,Figure 2.2| The electromagnetic frequency spectrum.第二章 固态原理 能量的这种价值也许会被呈现在更为普遍的电子伏特部件里（见附录D）。 这个电子伏特部件的能量单位等于1610-19J。我们可以写 n 注释：光子能跟波长的倒数关系证明：一个大能源对应一个短的波长。 练习题 例2.1：确定在电子伏特中的光子能有（a）和（b）的波长。 2.1.2 粒子波的对偶原理 我们在前一段落所看到的光波，在光电效应里表现得像是颗粒。在1924年，德布洛伊假定了物质波的存在。他暗示了，自从这种波展现出了类似微粒的行为，微粒就被指望有着波状的性能。德布洛伊的假设是波粒子对偶原理的存在。给出的光子动量是： （2.2）是光波的波长。而德布洛伊假设微粒的波长可以表示为： （2.3）P是指微粒动量，而被称为是德布洛伊的物质波波长。例2.2目标确定一个微粒的德布洛伊波长。 考虑一个电子以速度107cm/s=105m/s的运行。n 解决方案给出的动量为 P = mv =(9.1110-31)(105)=9.1110-26Kg-m/s而德布洛伊波长为 2.1 量子力学原理或 n 注释这个计算表明了一个“典型”电子的德布洛伊波长的数量级。 练习题 例2.2（a）找出质量为510-31Kg和德布洛伊波长为的微粒的动量和能量。 （b）一个电子拥有20meV的动能，确定它的德布洛伊波长。 在粒子波的对偶原理中获得一些有关频率和波长的鉴别，图2.2显示的是电磁频谱。在图2.2中我们看到的波长是