Summary of Quantum Mechanics
1 Principles
2 General Results
3 The Particular Case of a Point-Like Particle; Wave Mechanics.
4 Angular Momentum and Spin
5 Exactly Soluble Problems
6 Approximation Methods
7 Identical Particles
8 Time-Evolution of Systems
9 Collision Processes
Part I Elementary Particles, Nuclei and Atoms
Neutrino Oscillations
1.1 Mechanism of the Oscillations; Reactor Neutrinos
1.2 Oscillations of Three Species; Atmospheric Neutrinos
1.3 Solutions
1.4 Comments
2 Atomic Clocks
2.1 The Hyperfine Splitting of the Ground State
2.2 The Atomic Fountain
2.3 The GPS System
2.4 The Drift of Fundamental Constants
2.5 Solutions
3 Neutron Interferometry
3.1 Neutron Interferences
3.2 The Gravitational Effect
3.3 Rotating a Spin 1/2 by 360 Degrees
3.4 Solutions
4 Spectroscopic Measurement on a Neutron Beam
4.1 Ramsey Fringes
4.2 Solutions
5 Analysis of a Stern-Gerlach Experiment
5.1 Preparation of the Neutron Beam
5.2 Spin State of the Neutrons
5.3 The Stern-Gerlach Experiment
5.4 Solutions
6 Measuring the Electron Magnetic Moment Anomaly
6.1 Spin and Momentum Precession of an Electron in a Magnetic Field
6.2 Solutions Decay of a Tritium Atom
7.1 The Energy Balance in Tritium Decay
7.2 Solutions
7.3 Comments
The Spectrum of Positronium
8.1 Positronium Orbital States
8.2 Hyperfine Splitting
8.3 Zeeman Effect in the Ground State
8.4 Decay of Positronium
8.5 Solutions
The Hydrogen Atom in Crossed Fields
9.1 The Hydrogen Atom in Crossed Electric and Magnetic Fields
9.2 Pauli's Result
9.3 Solutions
10 Energy Loss of Ions in Matter
10.1 Energy Absorbed by One Atom
10.2 Energy Loss in Matter
10.3 Solutions
10.4 Comments
Part II Quantum Entanglement and Measurement
11 The EPR Problem and Bell's Inequality
11.1 The Electron Spin
11.2 Correlations Between the Two Spins
11.3 Correlations in the Singlet State
11.4 A Simple Hidden Variable Model
11.5 Bell's Theorem and Experimental Results
11.6 Solutions
12 Schrodinger's Cat
12.1 The Quasi-Classical States of a Harmonic Oscillator
12.2 Construction of a Schr5dinger-Cat State
12.3 Quantum Superposition Versus Statistical Mixture
12.4 The Fragility of a Quantum Superposition
12.5 Solutions
12.6 Comments
13 Quantum Cryptography
13.1 Preliminaries
13.2 Correlated Pairs of Spins
13.3 The Quantum Cryptography Procedure
13.4 Solutions
14 Direct Observation of Field Quantization
14.1 Quantization of a Mode of the Electromagnetic Field
14.2 The Coupling of the Field with an Atom
14.3 Interaction of the Atom with an "Empty" Cavity
14.4 Interaction of an Atom with a Quasi-Classical State
14.5 Large Numbers of Photons: Damping and Revivals
14.6 Solutions
14.7 Comments
15 Ideal Quantum Measurement
15.1 Preliminaries: a yon Neumann Detector
15.2 Phase States of the Harmonic Oscillator
15.3 The Interaction between the System and the Detector
15.4 An "Ideal" Measurement
15.5 Solutions
15.6 Comments
16 The Quantum Eraser
16.1 Magnetic Resonance
16.2 Ramsey Fringes
16.3 Detection of the Neutron Spin State
16.4 A Quantum Eraser
16.5 Solutions
16.6 Comments
17 A Quantum Thermometer
17.1 The Penning Trap in Classical Mechanics
17.2 The Penning Trap in Quantum Mechanics
17.3 Coupling of the Cyclotron and Axial Motions
17.4 A Quantum Thermometer
17.5 Solutions
Part III Complex Systems
18 Exact Results for the Three-Body Problem
18.1 The Two-Body Problem
18.2 The Variational Method
18.3 Relating the Three-Body and Two-Body Sectors
18.4 The Three-Body Harmonic Oscillator
18.5 From Mesons to Baryons in the Quark Model
18.6 Solutions
19 Properties of a Bose-Einstein Condensate
19.1 Particle in a Harmonic Trap
19.2 Interactions Between Two Confined Particles
19.3 Energy of a Bose-Einstein Condensate
19.4 Condensates with Repulsive Interactions
19.5 Condensates with Attractive Interactions
19.6 Solutions
19.7 Comments
20 Magnetic Excitons
20.1 The Molecule CsFeBra
20.2 Spin-Spin Interactions in a Chain of Molecules
20.3 Energy Levels of the Chain
20.4 Vibrations of the Chain: Excitons
20.5 Solutions
Quantum mechanics is an endless source of new questions and fascinating observations. Examples can be found in fundamental physics and in applied physics, in mathematical questions as well as in the currently popular debates on the interpretation of quantum mechanics and its philosophical implications.
Teaching quantum mechanics relies mostly on theoretical courses, which are illustrated by simple exercises often of a mathematical character. Reduc- ing quantum physics to this type of problem is somewhat frustrating since very few, if any, experimental quantities are available to compare the results with. For a long time, however, from the 1950s to the 1970s, the only alterna- tive to these basic exercises seemed to be restricted to questions originating from atomic and nuclear physics, which were transformed into exactly soluble problems and related to known higher transcendental functions.
In the past ten or twenty years, things have changed radically. The devel- opment of high technologies is a good example. The one-dimensional square- well potential used to be a rather academic exercise for beginners. The emer- gence of quantum dots and quantum wells in semiconductor technologies has changed things radically. Optronics and the associated developments in infra- red semiconductor and laser technologies have considerably elevated the social rank of the square-well model. As a consequence, more and more emphasis is given to the physical aspects of the phenomena rather than to analytical or computational considerations.
Many fundamental questions raised since the very beginnings of quantum theory have received experimental answers in recent years. A good example is the neutron interference experiments of the 1980s, which gave experimental answers to 50 year old questions related to the measurability of the phase of the wave function. Perhaps the most fundamental example is the experimen- tal proof of the violation of Bell's inequality, and the properties of entangled states, which have been established in decisive experiments since the late 1970s, More recently, the experiments carried out to quantitatively verify de- coherence effects and "SchrSdinger-cat" situations have raised considerable.