振动与波：概论（第二版）

本书的目标是发展一个关于振动和波的统一的数学理论。例子来自离散机械系统的物理学，连续的气体、流体和弹性固体，电子电路，电磁波，光学系统，最后是量子力学系统。
假设本书的读者对物理定律有基本的了解，比如他们可能是从标准的两学期的介绍性大学水平的调查课程中获得了相关知识。我们还假定读者熟悉大学水平的数学知识，包括代数、三角学、线性代数、常微分方程和偏微分方程。
本书的一个不同寻常的特征是对振动和波的传统复表示的介绍被推迟到了绝对必要时(在讨论量子力学波时)。这样安排的原因是，尽管振动和波的复表示极大地方便了计算，但它(至少在最初)是发展对此类现象的物理理解的重大障碍。作者认为，在尝试使用更方便、更抽象、更复杂的表示之前，学生应该先彻底地理解如何用正则三角函数来表示振动和波。
本书只讨论控制微分方程是线性的那一类振动和波。在大多数物理系统中，这意味着对相对低幅度现象的限制。作者抵制住了讨论非线性振动和波的诱惑，主要是因为这种现象需要用一种与描述线性振动和波完全不同的数学分析来讨论，而本书的重点是主题的数学统一性。

Preface
CHAPTER 1 Simple Harmonic Oscillation
1.1 Introduction
1.2 Mass on Spring
1.3 Simple Harmonic Oscillator Equation
1.4 LC Circuit
1.5 Simple Pendulum
1.6 Compound Pendulum
Exercises
CHAPTER 2 Damped and Driven Harmonic Oscillation
2.1 Introduction
2.2 Damped Harmonic Oscillation
2.3 Quality Factor
2.4 LCR Circuit
2.5 Driven Damped Harmonic Oscillation
2.6 Driven LCR Circuit
2.7 Transient Oscillator Response
Exercises
CHAPTER 3 Coupled Oscillations
3.1 Introduction
3.2 Two Spring-Coupled Masses
3.3 Two Coupled LC Circuits
3.4 Three Spring-Coupled Masses
Exercises
CHAPTER 4 Transverse Standing Waves
4.1 Introduction
4.2 Normal Modes of Beaded String
4.3 Normal Modes of Uniform String
4.4 General Time Evolution of Uniform String
Exercises
CHAPTER 5 Longitudinal Standing Waves
5.1 Introduction
5.2 Spring-Coupled Masses
5.3 Longitudinal Waves on Thin Elastic Rod
5.4 Sound Waves in Ideal Gas
5.5 Fourier Analysis
Exercises
CHAPTER6 Traveling Waves
6.1 Introduction
6.2 Standing Waves in Finite Continuous Medium
6.3 Traveling Waves in Infinite Continuous Medium
6.4 Wave Interference
6.5 Energy Conservation
6.6 Transmission Lines
6.7 Normal Reflection and Transmission at Interfaces
6.8 Electromagnetic Waves
6.9 Doppler Effect
6.10 Wave Propagation in Inhomogeneous Media
Exercises
CHAPTER 7 Multi-Dimensional Waves
7.1 Introduction
7.2 Plane Waves
7.3 Three-Dimensional Wave Equation
7.4 Cylindrical Waves
7.5 Spherical Waves
7.6 Oscillation of an Elastic Sheet
7.7 Polarization of Electromagnetic Waves
7.8 Laws of Geometric Optics
7.9 Fresnel Relations
7.10 Total Internal Reflection
7.11 Birefringence
7.12 Sound Waves in Fluids
Exercises
CHAPTER 8 Wave Pulses
8. l Introduction
8.2 Fourier Transforms
8.3 Dirac Delta Function
8.4 General Solution of 1D Wave Equation
8.5 Bandwidth
8.6 Bandwidth Theorem
Exercises
CHAPTER 9 Dispersive Waves
9.1 Introduction
9.2 Pulse Propagation
9.3 Electromagnetic Waves in Unmagnetized Plasmas
9.4 Faraday Rotation
95 Electromagnetic Waves in Magnetized Plasmas
9.6 Low-Frequency EM Waves in Magnetized Plasmas
9.7 Parallel EM Waves in Magnetized Plasmas
9.8 Perpendicular EM Waves in Magnetized Plasmas
9.9 Electromagnetic Waves in Conductors
9.10 Waveguides
9.11 Pulse Propagation in Two Dimensions
9.12 Giavity Waves
9.13 Wave Drag on Ships
9.14 Ship Wakes
9.15 Capillary Waves
Exercises
CHAPTER 10 Wave Optics
10.1 Introduction
10.2 Two-Slit Interference
10.3 Coherence
10.4 Multi-Slit Interference
10.5 Thin-Film Interference
10.6 One-Dimensional Fourier Optics
10.7 Single-Slit Diffraction
10.8 Multi-Slit Diffraction
10.9 Two-Dimensional Fourier Optics
10.10 Huygens-Fresnel Principle
10.11 Babinet’s Principle
10.12 Diffraction from Rectangular Aperture
10.13 Diffraction from Straight Edge
10.14 Diffraction from Rectangular Slit
10.15 Diffraction from Straight Wire
10.16 Diffraction from Circular Aperture
10.17 Diffraction from Circular Disk
Exercises
CHAPTER 11 Wave Mechanics
ll.l Introduction
11.2 Photoelectric Effect
11.3 Electron Diffraction
11.4 Representation of Waves via Complex Numbers
11.5 Schrtidinger’s Equation
11.6 Probability Interpretation of Wavefunction
11.7 Wave Packets
11.8 Heisenberg’s Uncertainty Principle
11.9 Wavefunction Collapse
11.10 Stationary States
11.11 Particle in Finite Square Potential Well
11.12 Square Potential Barrier
11.13 WKB Approximation
11.14 Cold Emission
11.15 Alpha Decay
11.16 Three-Dimensional Wave Mechanics
11.17 Particle in Box
11.18 Degenerate Electron Gas
11.19 White-Dwarf Star
Exercises
Bibliography
Index
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