Quantum Mechanics with Applications

Quantum Mechanics with Applications

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Product Details

ISBN-13: 9780486779904
Publisher: Dover Publications
Publication date: 10/15/2014
Series: Dover Books on Physics
Edition description: Reprint
Pages: 352
Product dimensions: 5.40(w) x 8.40(h) x 0.70(d)
Age Range: 18 Years

About the Author

David B. Beard (1922–98) was the University Distinguished Professor of Physics at the University of Kansas Department of Physics and Astronomy, where he taught for more than 20 years and served as Department Chairman from 1964 to 1977.
George B. Beard taught for 47 years at Wayne State University in the Department of Physics and Astronomy, where he served as Chair of the Physics and Computer Science departments and as Associate Dean.

Table of Contents

I Black Body Radiation 1

1.1 Derivation of the Electromagnetic Waves in a Cavity 1

1.2 Number of Modes Having the Same Frequency 5

1.3 The Radiation Energy Density 7

1.4 Significant Mathematical Processes Used in the Derivation 10

II Fourier Analysis 12

2.1 Fourier Series 14

2.2 Fourier Transforms 16

2.3 Relation Between the Width of a Function and its Transform 19

2.4 Wave Packets 21

III Diffraction and Interference of Photons and Particles 26

3.1 The Photoelectric Effect 27

3.2 The Compton Effect 29

3.3 Reconciliation of the Photon and Wave Theories of Light 30

3.4 Wave Characteristics of Particles 33

3.5 The Discreteness of Atomic Energy Levels 34

3.6 The Davisson-Germer Experiment 36

IV The Feynman Path Integrals and the Schrödinger Equation 39

4.1 Electron Diffraction 39

4.2 Diffraction of Light 42

4.3 Particle Probability Amplitudes 44

4.4 The Schrodinger Wave Equation 48

4.5 Particle Waves 51

V Use of the Wave Function to Obtain Physical Properties of a System 54

5.1 Observables 54

5.2 Commutation Relations 58

5.3 Particle Currents 62

5.4 Center of Mass Coordinates 63

VI One-Dimensional Problems 66

6.1 Particles Incident on a Square Barrier 67

6.2 Unbound and Bound Particles in a Square Well 73

6.3 The Linear Harmonic Oscillator 79

VII The WKB Approximation and the Bohr-Sommerfeld Quantum Conditions 83

7.1 The Wentzel-Kramers-Brillouin Method 84

7.2 Connection Formulas 87

7.3 Penetration Through a Barrier 90

VIII Elementary Three-Dimensional Wave Functions in Spherical Coordinates 94

8.1 General Method for Spherically Symmetric Potentials 95

8.2 Angular Momentum 97

8.3 Angular Momentum Commutation Relations 103

8.4 The Rigid Rotator 105

8.5 The Square Well 107

8.6 The Hydrogen Atom 110

8.7 The Harmonic Oscillator 114

IX Perturbation Theory 117

9.1 First-Order Perturbation Theory 120

9.2 The Helium Atom 123

9.3 Second-Order Perturbation Theory 126

9.4 Degenerate Levels 128

9.5 Dirac Bra and Ket Notation 130

9.6 Variational Method 130

X Time-Dependent Perturbation Theory 134

10.1 First-Order Time-Dependent Transition Probability 135

10.2 Excitation of Atoms by Ion Bombardment 138

10.3 Absorption of Radiation 140

10.4 General Selection Rules for Spherical Harmonic Wave Functions 141

10.5 Selection Rules for the Harmonic Oscillator Radial Quantum Number 144

10.6 The Hydrogen Atom 145

10.7 Emission 146

10.8 Second-Order Time-Dependent Perturbation Theory 148

10.9 Transitions to or from Unbound Systems 149

XI The One-Electron Atom 153

11.1 Energy Levels 155

11.2 Orbital Magnetic Moment 157

11.3 Precession in an External Magnetic Field 160

11.4 Force on a Dipole in a Non-Uniform Magnetic Field 161

11.5 Spin-Orbit Interaction 163

11.6 Relativistic Corrections 169

11.7 Spectroscopic Notation 170

11.8 Energy Level Diagrams 171

11.9 Zeeman and Paschen-Back Effects 171

11.10 Hyperfine Structure 178

XII Multi-Electron Atoms 183

12.1 Identical Particles - Symmetry 183

12.2 Helium Atom 188

12.3 Complex Atoms 192

12.4 Periodic Table 196

12.5 Spectroscopic Notation - Equivalent Electrons 198

12.6 Energy Levels 202

12.7 J-J Coupling 205

12.8 X Rays 207

XIII Molecular Structure 212

13.1 Ionic Binding 212

13.2 Covalent Binding - H+2Molecule 214

13.3 The Hydrogen Molecule (Heitler-London Treatment) 217

13.4 Spatial Orientation of Chemical Bonds 220

13.5 Diatomic Molecules 221

13.6 Comparison with Experiment - HCl 227

13.7 Effects of Nuclear Spin 228

13.8 Thermal Distribution of Vibrational and Rotational Levels 231

13.9 Raman Spectra 234

XIV Free Electron and Band Theory of Metals 236

14.1 Free Electron Theory 236

14.2 Band Theory 239

14.3 Effective Mass 243

XV Elastic Scattering Theory 247

15.1 The Path Integral Formulation of the Scattering Problem 249

15.2 General Formulation of Scattering Problems 251

15.3 The Born Approximation 252

15.4 Simple Applications of the Born Approximation 256

15.5 Qualitative Features of the Born Approximation 258

15.6 Atomic Scattering by the Born Approximation 258

15.7 Scattering by Identical Particles 260

15.8 The Method of Partial Waves 261

15.9 Scattering by Particle Waves of High Orbital Angular Momentum 266

15.10 Neutron-Proton Scattering 269

15.11 Effective Range Theory 271

XVI Nuclear Forces and Models 276

16.1 Nuclear Forces 277

16.2 The Individual Particle Model of the Nucleus 282

16.3 The Compound Nucleus 288

16.4 The Optical Model 290

16.5 The Collective or Unified Model 293

16.6 The Effective Mass of Nucleons Bound in a Potential 300

Appendix A The Vibrating String 302

Appendix B Matrices 305

Appendix C Reduction of Infinite Series in Higher Order Perturbation Theory 320

Appendix D Parity 322

Index 327

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