On the Theory of Quanta - Louis-Victor de Broglie (1892-1987)

A translation of :
RECHERCHES SUR LA TH´EORIE DES QUANTA
(Ann. de Phys., 10e s´erie, t. III (Janvier-F ´evrier 1925).
by: A. F. Kracklauer
c 􀀀AFK, 2004

Contents
List of Figures iii
Preface to German translation v
Introduction 1
Historical survey 2
Chapter 1. The Phase Wave 7
1.1. The relation between quantum and relativity theories 7
1.2. Phase and Group Velocities 10
1.3. Phase waves in space-time 12
Chapter 2. The principles of Maupertuis and Fermat 15
2.1. Motivation 15
2.2. Two principles of least action in classical dynamics 16
2.3. The two principles of least action for electron dynamics 18
2.4. Wave propagation; FERMAT’s Principle 21
2.5. Extending the quantum relation 22
2.6. Examples and discussion 23
Chapter 3. Quantum stability conditions for trajectories 27
3.1. BOHR-SOMMERFELD stability conditions 27
3.2. The interpretation of Einstein’s condition 28
3.3. Sommerfeld’s conditions on quasiperiodic motion 29
Chapter 4. Motion quantisation with two charges 33
4.1. Particular difficulties 33
4.2. Nuclear motion in atomic hydrogen 34
4.3. The two phase waves of electron and nucleus 36

CONTENTS

Chapter 5. Light
quanta 39
5.1. The atom of light 39
5.2. The motion of an atom of light 41
5.3. Some concordances between adverse theories of radiation 42
5.4. Photons and wave optics 46
5.5. Interference and coherence 46
5.6. BOHR’s frequency law. Conclusions 47
Chapter 6. X and g-ray diffusion 49
6.1. M. J. J. Thompson’s theory 49
6.2. Debye’s theory 51
6.3. The recent theory of MM. Debye and Compton 52
6.4. Scattering via moving electrons 55
Chapter 7. Quantum Statistical Mechanics 57
7.1. Review of statistical thermodynamics 57
7.2. The new conception of gas equilibrium 61
7.3. The photon gas 63
7.4. Energy fluctuations in black body radiation 67
Appendix to Chapter 5: Light quanta 69
Summary and conclusions 71
Bibliography 73

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