鄭海榮主編的這本《量子力學（英文版）》內容 包括初等量子力學的基本理論、基本構架及解決問題 的基本方法；量子理論在典型題中的應用；簡單近似 方法；全同粒子體系的量子理論；量子理論的最新進 展及實際應用舉例；動畫及模擬練習；問題討論與練 習。本書可作為高等學校的教材。
Preface前言Part I The Wave Function and Schr／Sdinger Equation第一部分 波函數(shù)及薛定諤方程 Chapter 1 The wave function and Schrodinger equation波函數(shù)和 Preface前言Part I The Wave Function and Schr／Sdinger Equation第一部分 波函數(shù)及薛定諤方程 Chapter 1 The wave function and Schrodinger equation波函數(shù)和薛定諤方程 1.1 The wave-particle duality and matter wave波粒二象性與物質波 1.2 Wave function and its statistical interpretation波函數(shù)及其統(tǒng)計解釋 1.3 The principle of superposition態(tài)疊加原理 1.4 The Schrodinger equation薛定諤方程 Biography人物檔案 Essay短文：SchrOdinger cat and EPR paradox薛定諤貓和EPR佯謬 Associated application相關應用：TEM and SEM透射及掃描電子顯微鏡 Animation and simulation演示與模擬 DiSCUSsion questions討論問題 Exercises習題 Chapter 2 Time-independent Schr6dinger equation and its application in one dimension定態(tài)薛定諤方程及其在一維問題中的應用 2.1 Time-independent Schr6dinger equation and the statmnary state定態(tài)薛定諤方程和定態(tài) 2.2 The bound state and discrete spectra束縛態(tài)與分立譜 2.3 Reflection and transmission，tunneling effect反射與透射，隧穿效應 Biography人物檔案 Associated application相關應用：STM掃描隧道顯微鏡 Animation and simulation演示與模擬 DiSCUSSion questions討論問題 Exercises習題Part II Physical Observables and Representations第二部分 可觀測物理量及表象理論 Chapter 3 Physical observables and representations可觀測量及其表示理論 3.1 Observables and operators力學量與算符 3.2 Eigenvalues and eigenvectors of Hermitian operators 厄米算符的本征值與本征矢量 3.3 Representations and their transformations表象理論與表象變換 3.4 The uncertainty principle不確定原理 3.5 Dirac notation and the occupation number representation狄拉克符號與占有數(shù)表象 Biography人物檔案 Essay短文：Heisenberg and matrix mechanics海森伯與矩陣力學 Animation and simulation演示與模擬 Discussion questions討論問題 Exercises習題Part III Appl ications of the Schr6dinger Equation in 3D第三部分 薛定諤方程在三維空間中的應用 Chapter 4 A particle in a central field 中心力場中的粒子 4.1 A particle in a central field 中心力場中的粒子 4.2 The radial equation for an electron in the Coulomb potential庫侖場中運動電子的徑向方程 4.3 The hydrogen atom氫原子 Biography人物檔案 Essay短文：Niels Bohr and his theory for the hydrOgen atom波爾和他的氫原子理論 Associated application相關應用：Quantum computer量子計算機 Discussion questions討論問題 Exercises習題Part IV Approximation Methods第四部分 近似方法 Chapter 5 Perturbation theory微擾理論 5.1 Time-independent perturbation theory定態(tài)微擾理論 5.2 Time-dependent perturbation theory含時微擾理論 5.3 The adiabatic theorem絕熱理論 Biography人物檔案 Essay短文：Berry phase Berry相位 Associated application相關應用：Laser激光 Animation and simulation演示與模擬 Discussion questions討論問題 Exercises習題Part V Spin and Identical Particle System第五部分 自旋和全同多粒子體系 Chapter 6 Spin and Identical Particle System自旋和全同粒子體系 6.1 The Stern-Gerlach experiment and its interpretation斯特恩-格拉赫實驗及其解釋 6.2 The description of spin 自旋的描述 6.3 The SchrOdinger equation of charged particles in an external electromagnetic field帶電粒子在外電磁場中的薛定諤方程 6.4 Total angular momentum總角動量 6.5 Fine structure of alkali atoms堿金屬原子的精細結構 6.6 The Zeeman effect塞曼效應 6.7 Characteristics of identical particles全同粒子的特征 6.8 The wave function for a system of identical particles全同粒子體系的波函數(shù) 6.9 WaVe functions for two-electron system兩電子體系的波函數(shù) 6.10 The helium atom氦原子 Biography人物檔案 Essay短文：Quantum entanglement and Bell theorem量子糾纏與Bell定理 Associated application相關應用：Bose-Einstein condensation玻色-愛因斯坦凝聚 Animation and simulation演示與模擬 Discussion questions討論問題 Exercises習題References參考文獻Appendices附錄Index索引
Part I The Wave Function and Schrodinger Equation
第一部分波函數(shù)及薛定諤方程
Chapter 1 The wave function and Schrodinger equation
波函數(shù)和薛定諤方程
The wave-particle duality and matter wave
波粒二象性與物質波
Particles and waves are two distinct entities in classical physics. As we have learned from both text books and daily experiences,a particle is a localized bundle of energy and momentum. At any tnstant, it can be described by state parameters,such as position q and momentum p (or velocity v if the mass is a constant). The parameters q and p evolve \n time according to some equations of motion,such as Newton’s law F = dp /dt. Given the tnitial values q (tz) and p (t ) at time tt, the position q (t) and momentum pit) at any time t can be deduced from the equations of motion. In contrast to the particle, a wave is considered as a periodic disturbance spread over space. It usually appears as some kind of periodic movement transferring energy from one point to another. A wave satisfies the superposition rules and presents jnterference and diffraction phenomena.
1.1.1 The wave-particle duality of light 光的波粒二象性
In the 17lh century, two competing theories of light were proposed during the debate about the nature of light: one was offered by Christian Huygens and the other by Isaac Newton. According to the theories,light was thought either to consist of waves (Huygens) or of corpuscles/particles (Newton). Huygens proposed that each point on a light wave front acted as a spherical point source
for the progressing wave. Newton’s argument satisfactorily and more simply
explained geometric optics and did not presume a medium for particle travel.At the beginning of 1 9lh century (801?1805),Thomas Young conducted the famous double-slit experiment showing that light from two slits interfere to produce a fringe pattern on a screen,a phenomenon that cannot be described by classical particles. In 1909?Geoffrey Ingram Taylor conducted an experiment that showed the interference phenomena by individual photons. The double-slit experiment has been repeated in many ways over the years and has become a standard demonstration of wave-like motion. But neither Newton nor Young were quite convincing about the nature of light. Light could not be described purely as a wave or as consisting of particles.
In 1900, Max Planck postulated that the energy of oscillators in a black body is an integer multiple of hv,where h is the Planck constant and v is the frequency of the oscillator. The problem was that the wave nature of light was widely accepted at that time,the concept have been completely formulated in Maxwell’s theory and confirmed by interference and diffraction experiments. After Planck’s quanta hypothesis, Albert Einstein postulated the concept of the photon to explain the photoelectric effect in 1 905, which also was used later to explain Compton scattering. According to Einstein’s assumption, electromagnetic radiation of frequency v consists of discrete units (quanta) of energy hv. That is, electromagnetic energy itself is quantized,and a single quantum is called photon.
Thus, mater can absorb energy from a monochromatic beam of light of
frequency v only in units of hv because the light arrives in the form of discrete quanta, each with energy hv. Einstein had re-introduced the problem of wave- particle duality for light! The relation between the light wave (v,A ) and the light photon (e,_p)is presented by the equations
where h is the Planck constant. Eqs (1.1.1) and (1.1.2) are called the Planck- Einstein relations,which reflect the wave-particle duality of light.
1.1.2 Matter wave and the wave -particle duality of matter 物質波及物質的波粒二象性
If the light could sometimes behave like particles, then should matter
particles also show wave-like behavior? Upon examining Einstein’s idea of the parallelism between the light and matter,Louis de Broglie in 1 924 proposed that
electrons,which generally are believed to be particles, should exhibit wave-like behavior. The wavelength and frequency of a quantum mechanical particle are associated with its momentum and energy by de Broglie’s hypothesis
Where e and p are the energy and momentum of the particle,and v represents the frequency. The wavelength of the matter wave associated with the particle, A, is also called de Broglie wavelength. In the case of non-relativistic theory,the de Broglie wavelength for a free particle with mass m and energy e is
The wave nature of an electron and de Broglie’s hypothesis have been experimentally confirmed by electron diffraction experiments by G. P. Thompson, and C. Davisson & L. Germer. In short, any matter must be considered as having both the particle-like and wave -like properties.
You may want to argue that common sense tells us that billiard balls and ping-pong balls travel along definite trajectories and do not show any wave-like properties! The point is that the wave nature of matter is not apparent for macroscopic phenomena since Planck’s constant h is so small. For example, s
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