Engineering Quantum Mechanics

Preface vii

PART I Fundamentals 1

1 Basic Quantum Mechanics 3

1.1 Measurements and Probability 3

1.2 Dirac Formulation 4

1.3 Brief Detour to Classical Mechanics 8

1.4 A Road to Quantum Mechanics 14

1.5 The Uncertainty Principle 21

1.6 The Harmonic Oscillator 22

1.7 Angular Momentum Eigenstates 29

1.8 Quantization of Electromagnetic Fields 35

1.9 Perturbation Theory 38

Problems 41

References 43

2 Basic Quantum Statistical Mechanics 45

2.1 Elementary Statistical Mechanics 45

2.2 Second Quantization 51

2.3 Density Operators 54

2.4 The Coherent State 58

2.5 The Squeezed State 62

2.6 Coherent Interactions Between Atoms and Fields 68

2.7 The Jaynes-Cummings Model 69

Problems 71

References 72

3 Elementary Theory of Electronic Band Structure in Semiconductors 73

3.1 Bloch Theorem and Effective Mass Theory 73

3.2 The Luttinger-Kohn Hamiltonian 84

3.3 The Zinc Blende Hamiltonian 105

3.4 The Wurtzite Hamiltonian 114

3.5 Band Structure of Zinc Blende and Wurtzite Semiconductors 123

3.6 Crystal Orientation Effects on a Zinc Blende Hamiltonian 135

3.7 Crystal Orientation Effects on a Wurtzite Hamiltonian 152

Problems 168

References 169

PART II Modern Applications 171

4 Quantum Information Science 173

4.1 Quantum Bits and Tensor Products 173

4.2 Quantum Entanglement 175

4.3 Quantum Teleportation 178

4.4 Evolution of the Quantum State: Quantum Information Processing 180

4.5 A Measure of Information 183

4.6 Quantum Black Holes 184

Appendix A: Derivation of Equation (4.82) 202

Appendix B: Derivation of Equations (4.93) and (4.106) 203

Problems 204

References 205

5 Modern Semiconductor Laser Theory 207

5.1 Density Operator Description of Optical Interactions 209

5.2 The Time-Convolutionless Equation 211

5.3 The Theory of Non-Markovian Optical Gain in Semiconductor Lasers 223

5.4 Optical Gain of a Quantum Well Laser with Non-Markovian Relaxation and Many-Body Effects 232

5.5 Numerical Methods for Valence Band Structure in Nanostructures 235

5.6 Zinc Blende Bulk and Quantum Well Structures 252

5.7 Wurtzite Bulk and Quantum Well Structures 258

5.8 Quantum Wires and Quantum Dots 265

Appendix: Fortran 77 Code for the Band Structure 274

Problems 286

References 287

Index 289