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目录第1章 叠加原理 1§1量子理论的需要 1§2光子的极化 1§3光子的干涉 7§4叠加与不确定性 10§5叠加原理的数学表达 14§6左矢量与右矢量 18第2章 动力学变量与可观察量 23§7线性算符 23§8共轭关系 26§9本征值与本征矢量 29§10可观察量 34§11可观察量的函数 41§12普遍的物理解释 45§13对易性与相容性 49第3章 表象理论 53§14基矢量 53§15 S函数 58§16基矢量的性质 62§17线性算符的表象 67§l8概率幅 72§19关于可观察量函数的若干定理 76§20符号的发展 79第4章 量子条件 84§21泊松括号 84§22薛定谔表象 89§23动量表象 94§24海森伯测不准原理 97§25位移箅符 99§26 幺正变换 103第5章 运动方程 108§27运动方程的薛定谔形式 108§28运动方程的海森伯形式 111§29定态 116§30自由粒子 118§31波包的运动 121§32作用量原理 125§33吉布斯系综 130第6章 初等应用 136§34谐振子 136§35角动量 140§36角动量的性质 144§37电子的自旋 149§38在有心力场中的运动 152§39氢原子的能级 156§40选择定则 159§41氢原子的塞曼效应 165第7章 微扰理论 167§42概述 167§43微扰引起的能级变化 168§44引起跃迁的微扰 172§45对辐射的应用 175§46与时间无关的微扰引起的跃迁 178§47反常塞曼效应 181第8章 碰撞问题 185§48概述 185§49散射系数 188§50动量表象中的解 193§51色散散射 199§52共振散射 201§53发射与吸收 204第9章 包含许多相同粒子的系统 207§54对称态与反对称态 207§55排列作为动力学变量 211§56排列作为运动恒量 213§57能级的决定 216§58对电子的应用 219第10章 辐射理论 225§59玻色子系集 225§60玻色子与振子之间的联系 227§61玻色子的发射与吸收 232§62对光子的应用 235§63光子与原子间的相互作用能 239§64辐射的发射、吸收与散射 244§65费米子系集 248第11章 电子的相对论性理论 253§66粒子的相对论性处理 253§67电子的波方程 254§68洛伦兹变换下的不变性 258§69 自由电子的运动 261§70 自旋的存在 263§71过渡到极坐标变量 267§72氢原子能级的精细结构 269§73正电子理论 273第12章 量子电动力学 276§74没有物质的电磁场 276§75量子条件的相对论形式 280§76 一个时刻的动力学变量 283§77补充条件 287§78电子与正电子 292§79相互作用 298§80物理的变量 302§81诠释 306§82应用 310索引 313CONTENTSI.THE PRINCIPLE OF SUPERPOSITION 11.The Need for a Quantum Theory 12.The Polarization of Photons 43.Interference of Photons 74.Superposition and Indeterminacy 105.Mathematical Formulation of the Principle 146.Bra and Ket Vectors 18II. DYNAMICAL VARIABLES AND OBSERVABLES 237.Linear Operators 238.Conjugate Relations 269.Eigenvalues and Eigenvectors 2910.Observables 3411.Functions of Observables 4112.The General Physical Interpretation 4513.Commutability and Compatibility 49III. REPRESENTATIONS 5314.Basic Vectors 5315.The 8 Function 5816.Properties of the Basic Vectors 6217.The Representation of Linear Operators 6718.Probability Amplitudes 7219.Theorems about Functions of Observables 7620.Developments in Notation 79IV. THE QUANTUM CONDITIONS 8421.Poisson Brackets 8422.Schrodinger‘8 Representation 8923.The Momentum Represantation 9424.Heisenberg’s Principb of Uncertainty 9725.Displacement Operators 9926.Unitary Transformations 103V. THE EQUATIONS OF MOTION 10827.Schrodinger‘s Form for the Equations of Motion 10828.Heisenberg’s Form for the Equations of Motion 11129.Stationary States 11630.The Free Particle 11831.The Motion of Wave Packets 12132.The Action Principle 12533.The Gibbs Ensemble 130VI. ELEMENTARY APPLICATIONS 13634.The Harmonic Oscillator 13635.Angular Momentum 14036.Properties of Angular Momontum 14437.The Spin of the Electron 14938.Motion in a Central Field of Force 15239.Energy Ievels of the Hydrogen Atom 15640.Selection Rules 15941.The Zeeman Effect for tYie Hydrogen Atom 165VII. PERTURBATION THEORY 16742.General Remarks 16743.The Change in the Energy levels caused by a Perturbation 16844.The Perturbation considered as ca.using Transitions 17245.Application to Radiation 17546.Transitions caused by a Perturbation Independent of the Time 17847.The Anomalous Zeeman Effect 181VIII. COLLISION PROBLFMS 18548.General Remarks 18549.The Scattering Coefficient 18850.Solution with the Momentum Representation 193 19951.Dispersive Scattering 19952.Resonance Scattering 20153.Emission and Absorption 204IX. SYSTEMS CONTAINING SEVERAL SIMILAR PARTICLES 20754.Symmetrical and Antisymmetrical States 20755.Permutations as Dynamical Variables 21156.Permutations as Constants of the Motion 21357.Determination of the Energy levels 21658.Application to Electrons 219X. THEORY OF RADIATION 22559.An Assembly of Bosons 22560.The Connexion between Bosons and Oscillators 22761.Emission and Absorption of Bosons 93262.Application to Photons 93563.The Interaction Energy between Photons and an Atom 23964.Emissioii， Absorption， and Scattering of Radiation 24465.An Assembly of Fermions 248XI. RELATIVISTIC THEORY OF THE ELECTRON 25366.Relativistic Treatment of a Particle 25367.TJw Wave Equation for the Electron 25468.Invariance under a Lorentz Transformation 25869.The Motion of a Free Electron 26170.Existence of the Spin 26371.Tranaition to Polar Variables 26772.The Fine structure of the Energy Ievels of Hydrogen 27373.Theory of the Positron 273Xii. QUANTUM ELECTRODYNAMICS 27674.The Electromagnetic F 16ld in the Ab
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第1章 叠加原理 1．量子理论的需要 CI丛S8ICAL mechanics has been developed continuously from the time of Newton and applied to an ever-widening range of dynamical systems， including the electromagnetic field in interaction with ruatter. The underlying ideas and the laws governing their applica-tion form a simple and elegant scheme， which one would be inclined to think could not be seriously modified without having all its attractive features spoilt.Nevertheless it has been found possible to set up a new scherue， called quantum mechanics， which is more suitable for the description of phenomena on the atomic scale and which is in some respects more elegant and satisfying than the classical scheme. This possibility is due to the changes which the new scher:ae involves being of a very profound character and not claslring with the features of the classical theory that make it so attractive， as a result of .vhich all these features can be incorporated in the new scheme. The necessity for a departure from classical mechanics is clearly shown by experimental results. In the first place the forces known in classical electrodynamics are inadequate for the explanation of the remarkable stability of atoms and molecules， which is necessary in order that materials may have any definite physical and chemical properties at all.The introduction of new hypothetical forces will not save the situation， since there exist general principles of classical mechanics， holding for all kinds of forces， leading to results in d:irect disagreement with observation.For example， if an ato:tuic system has its eqllilibrium disturbed in any way and is then left alone， it wiU be set in oscillation and the oscillations will get impressed on the surround-ing electromagnetic field， so that their frequencies may be observed with a spectroscope.Now whatever the laws of force governing the equilibrium， one would expect to be able to include the various fre-quencies in a scheme comprising certain fundamental frequencies and their harmonics.Thi8 is not observed to be the case.Instead， there is observed a new and unexpected connexion between the frequencies， called Ritz‘s Combination Law of Spectroscopy， according to wliich all the frequencies can be expressed as di铂rences between certain terms， the number of terms being much less than the number of frequencies.This law is quite uninteDigible from the classical standpoint. One might try to get over the difficulty without departing from classical mechanics by assuming each of the spectroscopically ob-served frequencies to be a fundamental frequency with its own degree of freedom， the laws of force being such that the harmonic vibrations do not occur.Such a theory will not do， however， even apart from the fact that it would give no explanation of the Combination Law， since it would immediately bring one into conflict with the experi-mental evidence on specific heats. Classical statistical mechanics enables one to establish a general connexion ’oetween the total number of degrees of freedom of an assembly of vibrating systems and its specific heat. If one assumes all the spectroscopic frequencies of an atom to correspond to different degrees of freedom， one would get a specific heat for any kind of matter very much greater than the observed value. In fact the observed specific heats at ordinary temperatures are given fairly well by a theory that takes into account merely the motion of each atom as a whole and assigns no internal motion to it at all. This leads us to a new clash between classical mechanics and the result.s of experiment.There must certainly be some internal motion in an atom to account for its spectrum， but the internal degrees of freedom， for some classically inexplicable reason， do not contribute to the specific heat. A similar clash is found in connexion with the energy of oscillation of the electromagnetic fieldin a vacuum.Classical mechanics requires the specific heat corresponding to this energy to be infinite， but it is observed to be quite finite.A general conclusion from experimental results is that oscillations of high frequency do not contribute their classical quota to the specific heat. As another illustration of the failure of classical mechanics we may consider the behaviour of light. We have， on the one hand， the phenomena of interference and diffraction， which can be explained only on the oasis of a wave theory; on the other， phenoruena such as photo-electric emission and scattering by free electrons， which show that light is composed of smalJ particles. These particles， which are called photons， have each a defirute energy and momentum， de-pending on the frequency of the light， and appear to have just as real an existence as electrons， or any other particles known in physics. A fraction of a photon is never observed. Experiments have shown that this anomalous behaviour is not peculiar to light， but is quite general. All material particles have wave prop
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