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### Concepts of Modern Physics

Concepts of Modern Physics

Arthur Beiser

242 pages

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Preface

This book is intended for use with one-semester courses in modern physics that have elementary classical physics and calculus as prerequisites. Relativity and quantum theory are considered first to provide a framework for understanding the physics of atoms and nuclei. The theory of the atom is then developed with emphasis on quantum-mechanical notions, and is followed by a discussion of the properties of aggregates of atoms. Finally atomic nuclei and elementary particles are examined elementary driving-point and transfer function synthesis procedures. In Chapter 12, some fundamental concepts in modern filter design are introduced. Chapter 13 deals with the use of scattering matrices in network analysis and synthesis. In addition, there are three appendices covering the rudiments of matrix algebra, complex variables, and proofs of Brune's realizability theorems.

The balance here deliberately leans more toward ideas than toward experimental methods and practical applications. because I believe that the beginning student is better served in his introduction to modern physics by a conceptual framework than by a mass of individual details. However, all physical theories live or die by the sword of experiment, and a number of extended derivations are included in order lo demonstrate exactly how an abstract concept can lie related to actual measurements. Many instructors will prefer not to hold their students responsible for the more complicated (though not necessarily mathematically difficult) discussions, and I have indicated with asterisks sections that can be passed over lightly without loss of continuity; problems based on the contents of these sections are also marked with asterisks. Other omissions are also possible, of course. Relativity, For example, may well have teen covered earlier, and Part 3 in its entirety may be skipped when its contents will lie the subject of later work. Thus there is scope for an instructor to fashion the type of course he wishes, whether a general survey or a deeper inquiry into selected subjects, and to choose the level of treatment appropriate to his audience.

An expanded version of this book requiring no higher degree of mathematical preparation is my Perspectives of Modern Physics, an Upper Division Text in this series; other Upper Division Texts carry forward specific aspects of modem physics in detail.

TOC

Chapter I Special Relativity 3

1.1 The Michelson-Morlcy Experiment3

1.2 The Special Theory of Relativity g

1.3 Time Dilation 12

1.4 The Twin Paradox 16

1.5 length Contraction 17

1.6 Meson Decay 20

1.7 The Lorentz Transformation 22

1.8 The Inverse Lorentj; Transformation 27

1.9 Velocity Addition 28

1.10 The Relativity of Mass 30

1.11 Mass and Energy 35

1.12 Mass and Energy: Alternative

Derivation 37

Problems 39

Chapter 2 Particle Properties of Waves 43

2.1 The Photoelectric Effect 43

2.2 The Quantum Theory of light 47

2.3 X Rays 51

2.4 X-Ray Diffraction 56

2.5 The Compton Effect 60

2.6 Pair Production 63

2.7 Gravitational Red Shift 68

Problems 70

Chapter 3 Wave Properties of

Particles

3.1 De Broglie Waves

3.2 Wave Function

3.3 De Broglie Wave Velocity

3.4 Phase and Croup Velocities

3.5 The Diffraction of Particles

3.6 The Uncertainty Principle

3.7 Applications of the Uncertainty

Principle

3.8 The Wave-particle Duality

Problems

Chapter 4 Atomic Structure

4.1 Atomic Models

4.2 Alpha-particle Scattering

4.3 The Rutherford Scattering Formula

4.4 Nuclear Dimensions

4.5 Electron Orbits

4.6 Atomic Spectra

4.7 The Bohr Atom

4.8 Energy levels and Spectra

4.9 Nuclear Motion

4.10 Atomic Excitation

4.11 The Correspondence Principle Problems

Chapter 5 Quantum Mechanics

5.1 Introduction to Quantum Mechanics

5.2 The Wave Equation

5.7 The Particle in u Bus: Wave Functions

5.8 The Particle in a Nonrigid Box

5.10 The Harmonic Oscillator: Solution of Schrddioger's Equation

Problems

Chapter 6 Quantum Theory of the

Hydrogen Atom

6.1 Schrodinger's Equation for the Hydrogen Atom

6.2 Separation of Variables

6.3 Quantum Numbers

6.4 Principal Quantum Number

6.5 Orbital Quantum Number

6.9 Radiative Transitions

Problems

Chapter 7 Many-electron Atoms

7.1 Electron Spin

7.2 Spin -orbit Coupling

7.3 The Exclusion Principle

7.5 The Periodic Table

7.6 Hund's Rule

7.7 Total Angular Momentum

7.9 ft Coupling

7.10 One-electron Spectra

7.1 1 Two-electron Spectra

7.12 X-ray Spectra

Problems

Chapter 8 The Physics of Molecules

8.1 Molecular Function 243

8.5 Molecular Orbital 254

8.6 Hybrid Orientals 261

8.7 Carbon-carbon Bonds 265

8.8 Rotational Energy Levels 269

8.9 Vibrations Energy Levels 272

8.10 Electronic Spectra of Molecules

Chapter 9 Statistical Mechanics 287

Evaluation of Constant 293

9.5 Molecular Energies in an Ideal Gas 295

9.6 Rotutional Spectra 298

9.7 Rose-Einstein Distribution 300

9.8 Rluck-hody RadUlimi 3tM

9.9 Fcnni-Dirac Distribution M)

9.10 Comparison of Results 310

9.11 The Laser 311

Problems 314

Chapter 10

10 The Solid State 317

10.1 Crystalline and Amorphous Solids 317

10.2 Ionic Crystals 318

10.3 Covalent Crystals 325

111.4 Van Dcr Waals Forces 327

10.5 The Metallic Braid 331

10.6 The Rand Theory of Solids 333

10.7 The Fermi Bong1 339

10.8 Electron-energy Distribution 342

10.9 Rrtllouin Zones 344

10.11) Origin y( Forhiddcn Bands 346

10.11 Effect ive Mass 355

Problems 355

Chapter 1 1 The Atomic Nucleus 361

1 1.1 Atomic Masses 361

11.2 The Neutron 384

11.3 Stable Nuclei 386

11.4 Nuclear Sizes and Shapes 370

11.5 Binding Energy 372

11.8 The Dcuteron 374

1 1.7 Ground Stale of the Dculcrun 377

11.8 Triplet and Singlet States 379

1 1.8 The Liquid-drop Model 380

11.10 The Shell Model 383

Prohlems 397

Chapter 12 Nuclear Transformations 389

12.1 Radioactive Decay 389

12.2 Radioactive Scries 393

12.3 Alpha Decay 396

12.4 Barrier Penetration 399

12.5 Theory of Alpha Decay 404

12.8 Reta Decay 408

12.7 Inverse Reta Decay 411

12.8 Camma Decay 412

12.9 Cross Section

12.10 The Compound Nucleus

12.12 Trausuranic Elements

12.13 Thermonuclear Energy

Chapter 13 Elementary Particles

13.1 Antiparticlcs

13.2 Meson Theory of Nuclear Forces

13.3 Piraiv and Muons

13.4 Kaons and Ilyperons

13.5 Systematic* of Elementary Particles

13.6 Strangeness Number

13.7 Isotoptc Spin

13.9 Theories of Elementary Particles Problems

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