Bridging the gap between traditional books on quantum and statistical physics, this series is an ideal introductory course for students who are looking for an alternative approach to the traditional academic treatment. This pedagogical approach relies heavily on scientific or technological applications from a wide range of fields. For every new concept introduced, an application is given to connect the theoretical results to a real-life situation. Each volume features in-text exercises and detailed solutions, with easy-to-understand applications. This first volume sets the scene of a new physics. It explains where quantum mechanics come from, its connection to classical physics and why it was needed at the beginning of the twentieth century. It examines how very simple models can explain a variety of applications such as quantum wells, thermoluminescence dating, scanning tunnel microscopes, quantum cryptography, masers, and how fluorescence can unveil the past of art pieces.
Author(s): Jean-Michel Gillet
Publisher: World Scientific Publishing
Year: 2018
Language: English
Pages: 300
City: London
Contents
Preface
About the Author
Part I Experimental Puzzles and Birth of a New Constant in Physics
Chapter 1. From Waves to Particles
1.1 Short Wavelength Issue in Black-Body Radiation
1.1.1 Applications of black-body radiation
1.2 Frequency Dependence of Photoelectricity
1.2.1 Applications of the photoelectric effect
1.3 Compton, Checking on Electrons’ Speed
1.3.1 Applications and illustrations of Compton scattering
Chapter 2. From Particles to Wave Fields
2.1 Bohr Orbits Ground-Breaking Model
2.1.1 Applications of atomic radiation spectra
2.2 Louis de Broglie Introduces Particle Waves
2.3 The Franck and Hertz Energy Loss Experiment
2.4 Davisson and Germer Diffract Matter Particles
2.4.1 Applications of massive particles diffraction
Part II From Phenomenology to an Axiomatic Formulation of Quantum Physics
Chapter 3. A Heuristic Approach to Quantum Modelling
3.1 Waves as We Know Them: Let There Be Light
3.1.1 The medium
3.1.2 The energy
3.1.3 The waves
3.2 Matter Wave: Function and Consequences
3.2.1 A wavefunction to describe particles
3.2.2 Wavefunctions as plane waves or wave packets
3.3 A Wave Equation: The Schrödinger Equation
3.3.1 Mean position, mean potential
3.3.2 Mean momentum, mean kinetic energy
3.3.3 Mean total energy
3.3.4 The Schrödinger equation and its operators
3.3.5 Stationary solutions to Schrödinger’s equation
3.3.6 General solution to Schrödinger’s equation
3.4 Stationary States in One Dimension
Chapter 4. Piecewise Constant Potentials
4.1 Potential Jumps and Infinite Forces
4.2 On Wavefunction Continuity
4.3 Infinite Well
4.4 Potential Step
4.4.1 Going down
4.4.2 Going up
4.5 Finite Square Well: Bound and Unbound States
4.6 An Application of Quantum Wells: Thermoluminescence and Dating
4.7 Potential Barrier
4.8 The Jeffreys–Wentzel–Kramers–Brillouin Approximation and Non-constant Barriers
4.9 Applications of the Tunnel Transmission
4.9.1 The tunnel effect at two energy scales
4.9.2 The scanning tunnelling microscope
Chapter 5. Quantum Postulates and Their Mathematical Artillery
5.1 New Game, New Rules
5.1.1 Representation of a physical state
5.1.2 Physical quantities and operators
5.1.3 Results of measurements
5.1.4 Probability of a measurement outcome
5.1.5 Collapse of the wave packet
5.1.6 Time evolution of a state vector
5.2 The Mathematical Artillery
5.2.1 State space and kets
5.2.2 Operators
5.2.3 Mean values and generalized indetermination
5.3 An Application of Measurement Postulates to Quantum Cryptography
5.3.1 The secret correspondence between Alice and Bob
5.3.2 A measurement that leaves its mark
5.3.3 Sharing a quantum key
5.3.4 Spy, are you there?
5.4 Time Evolution of a State Ket
5.4.1 General implications of the evolution postulate
5.4.2 Application of a tunnelling dynamics to the MASER
Part III A Classical to Quantum World Fuzzy Border
Chapter 6. Phase Space Classical Mechanics
6.1 Lagrangian and “Least Action Principle”
6.1.1 Lagrange’s equations
6.2 From Lagrange to Hamilton
6.3 Constrained Trajectories
6.3.1 From holonomic constraint. . .
6.3.2 ... to Lagrange multipliers
6.4 From Hamilton to Hamilton–Jacobi
6.5 Reconnecting to Quantum Physics
Chapter 7. Quantum Criteria (Who Needs Quantum Physics?)
7.1 Ehrenfest’s Theorem
7.2 Transition from Quantum to Classical Hamilton–Jacobi’s Equation
7.3 Particle Trajectories or Wave Interference?
7.3.1 Large quantum numbers and Bohr’s correspondence principle
7.3.2 The noticeable interferences criterion
7.3.3 The propagator and the multiple paths of a quantum particle
Bibliography
Index
