Introduction to Quantum Mechanics 1

The conception of lasers and optoelectronic devices such as solar cells have been made possible, thanks to the modern day mastery of processes that harness the interaction of electromagnetic radiation with matter.

This first volume is dedicated to thermal radiation and experimental facts that reveal the quantification of matter. The study of black body radiation allows the introduction of fundamental precepts such as Planck s law and the energy-related qualities that characterize radiation. The properties of light and wave particle duality are also examined, based on the interpretation of light interferences, the photoelectric effect and the Compton effect.

This book goes on to investigate the hydrogen atomic emission spectrum and how it dovetails into our understanding of quantum numbers to describe the energy, angular momentum, magnetic moment and spin of an electron. A look at the spectroscopic notation of the states explains the different wavelengths measured from the splitting of spectral lines.

Finally, this first volume is completed by the study of de Broglie s wave theory and Heisenberg s uncertainty principle, which facilitated the advancement of quantum mechanics.

Auteur
Ibrahima Sakho is a Doctor of Physical Science, and works at the science and technology training and research unit at the University of Thies (Senegal). On-site, he teaches quantum mechanics, atomic and nuclear physics, radiation?matter interaction, and environmental chemistry.

Contenu

Foreword xi
Louis MARCHILDON

Preface xiii

Chapter 1. Thermal Radiation 1

1.1. Radiation 2

1.1.1. Definition 2

1.1.2. Origin of radiation 2

1.1.3. Classification of objects 4

1.2. Radiant flux 4

1.2.1. Definition of radiant flux, coefficient of absorption 4

1.2.2. Black body and gray body 5

1.3. Black body emission spectrum 6

1.3.1. Isotherms of a black body: experimental facts 6

1.3.2. Solid angle 7

1.3.3. Lambert's law, radiance 9

1.3.4. Kirchhoff's laws 10

1.3.5. StefanBoltzmann law, total energy exitance 11

1.3.6. Wien's laws, useful spectrum 12

1.3.7. The RayleighJeans law, ultraviolet catastrophe 15

1.3.8. Planck's law, monochromatic radiant exitance 16

1.4. Exercises 18

1.4.1. Exercise 1 Calculation of the StefanBoltzmann constant 18

1.4.2. Exercise 2 Calculation of the Sun's surface temperature 18

1.4.3. Exercise 3 Average energy of a quantum oscillator, Planck's formula 19

1.4.4. Exercise 4 Deduction of Wien's first law from Planck's formula 20

1.4.5. Exercise 5 Total electromagnetic energy radiated by the black body 20

1.5. Solutions 21

1.5.1. Solution 1 Calculation of the StefanBoltzmann constant 21

1.5.2. Solution 2 Calculation of the Sun's surface temperature 23

1.5.3. Solution 3 Average energy of a quantum oscillator, Planck's formula 24

1.5.4. Solution 4 Deduction of Wien's law from Planck's law 27

1.5.5. Solution 5 Total electromagnetic energy radiated by the black body 29

Chapter 2. Wave and Particle Aspects of Light 33

2.1. Light interferences 34

2.1.1. Elongation of a light wave 34

2.1.2. Total elongation of synchronous light sources 35

2.1.3. Young's experimental setup 36

2.1.4. Interference field, fringes of interference 37

2.1.5. Interpretation, interference as concept 37

2.1.6. Path difference 39

2.1.7. Fringe spacing, order of interference 41

2.2. Photoelectric effect 44

2.2.1. Experimental setup, definition 44

2.2.2. Interpretation, photon energy 44

2.2.3. Einstein relation, energy function 45

2.2.4. Photoelectric threshold 46

2.2.5. Stopping potential, saturation current 48

2.2.6. Quantum efficiency of a photoelectric cell 51

2.2.7. Sensitivity of a photoelectric cell 51

2.3. Compton effect 53

2.3.1. Experimental setup, definition 53

2.3.2. Energy and linear momentum of a relativistic particle 55

2.3.3. Interpretation, photon linear momentum, and Compton shift 56

2.4. Combining the particle- and wave-like aspects of light 59

2.4.1. Particle- and wave-like properties of the photon 59

2.4.2. PlanckEinstein relation 60

2.5. Exercises 61

2.5.1. Exercise 1 Single-slit diffraction, interferences 61

2.5.2. Exercise 2 Order of interference fringes 62

2.5.3. Exercise 3 Experimental measurement of Planck constant and of the work function of an emissive photocathode 63

2.5.4. Exercise 4 Experimental study of the behavior of a photoelectric cell, quantum efficiency and sensitivity 64

2.5.5. Exercise 5 Compton backscattering 65

2.5.6. Exercise 6 Energy and linear momentum of scattered photons and of the electron ejected by Compton effect 65

2.5.7. Exercise 7 Inverse Compton effect 66

2.6. Solutions 66

2.6.1. Solution 1 Single-slit diffraction, interferences 66

2.6.2. Solution 2 Order of interference fringes 68

2.6.3. Solution 3 Experimental measurement of Planck constant and of the work function of an emissive photocathode 70

2.6.4. Solution 4 Experimental study of the behaviour of a photoelectric cell, quantum efficiency and sensitivity 74

2.6.5. Solution 5 Compton backscattering 76 2.6.6. Solution 6 Energy and linear momentum of the scatte...