Table of Contents
Preface v
About the Author xi
Part I Experimental Puzzles and Birth of a New Constant in Physics 1
Chapter 1 From Waves to Particles 7
1.1 Short Wavelength Issue in Black-Body Radiation 8
1.1.1 Applications of black-body radiation 16
1.2 Frequency Dependence of Photoelectricity 18
1.2.1 Applications of the photoelectric effect 24
1.3 Compton, Checking on Electrons' Speed 25
1.3.1 Applications and illustrations of Compton scattering 29
Chapter 2 From Particles to Wave Fields 35
2.1 Bohr Orbits Ground-Breaking Model 36
2.1.1 Applications of atomic radiation spectra 39
2.2 Louis de Broglie Introduces Particle Waves 47
2.3 The Franck and Hertz Energy Loss Experiment 49
2.4 Davisson and Germer Diffract Matter Particles 51
2.4.1 Applications of massive particles diffraction 56
Part II From Phenomenology to an Axiomatic Formulation of Quantum Physics 63
Chapter 3 A Heuristic Approach to Quantum Modelling 67
3.1 Waves as We Know Them: Let There Be Light 68
3.1.1 The medium 69
3.1.2 The energy 71
3.1.3 The waves 73
3.2 Matter Wave: Function and Consequences 83
3.2.1 A wavefunction to describe particles 83
3.2.2 Wavefunctions as plane waves or wave packets 89
3.3 A Wave Equation: The Schrödinger Equation 97
3.3.1 Mean position, mean potential 97
3.3.2 Mean momentum, mean kinetic energy 101
3.3.3 Mean total energy 102
3.3.4 The Schrödinger equation and its operators 103
3.3.5 Stationary solutions to Schrödinger's equation 108
3.3.6 General solution to Schrödinger's equation 110
3.4 Stationary States in One Dimension 113
Chapter 4 Piecewise Constant Potentials 117
4.1 Potential Jumps and Infinite Forces 118
4.2 On Wavefunction Continuity 119
4.3 Infinite Well 121
4.4 Potential Step 127
4.4.1 Going down 128
4.4.2 Going up 131
4.5 Finite Square Well: Bound and Unbound States 132
4.6 An Application of Quantum Wells: Thermoluminescence and Dating 137
4.7 Potential Barrier 140
4.8 The Jeffreys-Wentzel-Kramers-Brillouin Approximation and Non-constant Barriers 145
4.9 Applications of the Tunnel Transmission 147
4.9.1 The tunnel effect at two energy scales 147
4.9.2 The scanning tunnelling microscope 152
Chapter 5 Quantum Postulates and Their Mathematical Artillery 161
5.1 New Game, New Rules 163
5.1.1 Representation of a physical state 164
5.1.2 Physical quantities and operators 165
5.1.3 Results of measurements 166
5.1.4 Probability of a measurement outcome 167
5.1.5 Collapse of the wave packet 168
5.1.6 Time evolution of a state vector 170
5.2 The Mathematical Artillery 171
5.2.1 State space and kets 172
5.2.2 Operators 178
5.2.3 Mean values and generalized indetermination 199
5.3 An Application of Measurement Postulates to Quantum Cryptography 206
5.3.1 The secret correspondence between Alice and Bob 207
5.3.2 A measurement that leaves its mark 207
5.3.3 Sharing a quantum key 209
5.3.4 Spy, are you there? 211
5.4 Time Evolution of a State Ket 215
5.4.1 General implications of the evolution postulate 215
5.4.2 Application of a tunnelling dynamics to the MASER 219
Part III A Classical to Quantum World Fuzzy Border 231
Chapter 6 Phase Space Classical Mechanics 235
6.1 Lagrangian and "Least Action Principle" 235
6.1.1 Lagrange's equations 236
6.2 From Lagrange to Hamilton 238
6.3 Constrained Trajectories 245
6.3.1 From holonomic constraint 245
6.3.2 … to Lagrange multipliers 247
6.4 From Hamilton to Hamilton-Jacobi 247
6.5 Reconnecting to Quantum Physics 250
Chapter 7 Quantum Criteria (Who Needs Quantum Physics?) 255
7.1 Ehrenfest's Theorem 256
7.2 Transition from Quantum to Classical Hamilton-Jacobi's Equation 262
7.3 Particle Trajectories or Wave Interference? 266
7.3.1 Large quantum numbers and Bohr's correspondence principle 266
7.3.2 The noticeable interferences criterion 267
7.3.3 The propagator and the multiple paths of a quantum particle 270
Bibliography 275
Index 281
