Quantum Mechanics

by David B Beard

Overview

This text appeals to readers' intuitive grasp of the wave theory of light, explaining how quantum mechanics arises from the diffraction and interference experiments in the same manner of physical optics. Coherent examples explore the quantum mechanical analog of classical quantities, and the entire work examines the physical meanings of the theory and its applications.
Providing a semester's worth of introductory material, this treatment explores quantum mechanics in a balanced, integrated manner. Subjects explored in the introductory chapters were chosen for their mathematical simplicity. Physical applications stressed in later chapters will prepare students for topics they are likely to encounter early in further studies of atomic and nuclear physics.

Product Details

ISBN-13:	9780486779928
Publisher:	Dover Publications
Publication date:	10/22/2014
Series:	Dover Books on Physics Series
Pages:	336
Product dimensions:	5.40(w) x 8.40(h) x 0.80(d)

About the Author

David B. Beard (1922–98) was the University Distinguished Professor of Physics at the University of Kansas, where he taught for more than 20 years and served as Chairman of the Department of Physics and Astronomy from 1964 to 1977.

Table of Contents

1 Black Body Radiation

1.1 Derivation of the Electromagnetic Waves in a Cavity 1

1.2 Number of Modes Having the Same Frequency 6

1.3 The Radiation Energy Density 8

1.4 Significant Mathematical Processes Used in the Derivation 12

2 Fourier Analysis

2.1 Fourier Series 17

2.2 Fourier Transforms 20

2.3 Relation Between the Width of a Function and its Transform 23

2.4 Wave Packets 26

3 Diffraction and Interference of Photons and Particles

3.1 The Photoelectric Effect 34

3.2 The Compton Effect 36

3.3 Reconciliation of the Photon and Wave Theories of Light 38

3.4 Wave Characteristics of Particles 41

3.5 The Discreteness of Atomic Energy Levels 43

3.6 The Davisson-Germer Experiment 45

4 The Feynman Path Integrals and the Schroedinger Equation

4.1 Electron Diffraction 49

4.2 Diffraction of Light 52

4.3 Particle Probability Amplitudes 54

4.4 The Schroedinger Wave Equation 56

4.5 Particle Waves 64

5 Use Of The Wave Function to Obtain Physical Properties of a System

5.1 Observables 67

5.2 Commutation Relations 71

5.3 Particle Currents 77

5.4 Center of Mass Coordinates 78

6 The Consequences of Abrupt Changes in Potential Energy

6.1 Particles Incident on a Square Barrier 85

6.2 Unbound and Bound Particles in a Square Well 93

6.3 The Band Theory of Metals 99

7 The wkb Approximation and the Bohr-Sommerfeld Quantum Conditions

7.1 The Wentzel-Kramers-Brillouin Method 110

7.2 Connection Formulas 113

7.3 The Bohr-Sommerfeld Quantum Conditions 117

7.4 Penetration Through a Barrier 121

8 Elementary Three-Dimensional Wave Functions in Spherical Coordinates

8.1 General Method for Spherically Symmetric Potentials 126

8.2 Angular Momentum 129

8.3 Angular Momentum Commutation Relations 136

8.4 The Rigid Rotator 139

8.5 The Square Well 141

8.6 The Hydrogen Atom 146

8.7 The Harmonic Oscillator 150

9 Perturbation Theory

9.1 First-Order Perturbation Theory 161

9.2 The Helium Atom 164

9.3 Second-Order Perturbation Theory 169

9.4 Degenerate Levels 171

9.5 Fine Structure 175

9.6 Variational Method 179

10 Time-Dependent Perturbation Theory

10.1 First-Order Time-Dependent Transition Probability 184

10.2 Excitation of Atoms by Ion Bombardment 188

10.3 Absorption of Radiation 190

10.4 General Selection Rules for Spherical Harmonic Wave Functions 192

10.5 Selection Rules for the Harmonic Oscillator Radial Quantum Number 196

10.6 The Hydrogen Atom 197

10.7 Emission 198

10.8 Second-Order Time-Dependent Perturbation Theory 201

10.9 Transitions to or from Unbound Systems 203

11 Chemical Resonance Theory

11.1 Review of Classical Coupled Oscillators 209

11.2 Quantum Mechanical Coupled Harmonic Oscillators 212

11.3 Change in Notation 216

11.4 The Helium Atom 217

11.5 The Hydrogen Molecule (Heitler-London Treatment) 222

11.6 Electrostatic Interaction Between Two Electrons In General 227

11.7 Relative Significance of the Several Atomic Interactions 229

12 Spin, Symmetry, Parity, and Vector Addition

12.1 Matrices of Angular Momentum 235

12.2 Spin 238

12.3 The Pauli Theory of Spin 242

12.4 Symmetry 245

12.5 Parity 249

12.6 Vector Addition Coefficients 254

13 Elastic Scattering Theory

13.1 The Path Integral Formulation of the Scattering Problem 265

13.2 General Formulation of Scattering Problems 268

13.3 The Born Approximation 269

13.4 Simple Applications of the Born Approximation 274

13.5 Qualitative Features of the Born Approximation 277

13.6 Atomic Scattering by the Born Approximation 277

13.7 Scattering by Identical Particles 280

13.8 The Method of Partial Waves 281

13.9 Scattering by Particle Waves of High Orbital Angular Momentum 288

13.10 Effective Range Theory 291

Appendix: The Vibrating String 299

Index 303