The Quantum Mechanics Solver: How to Apply Quantum Theory to Modern Physics

Preface to the Third Edition
Acknowledgements
Contents
Part I Elementary Particles, Nuclei and Atoms
	1 Matter-Wave Interferences with Molecules
		1.1 Helium Dimers and Trimers
		1.2 Interferences of Large Material Particles
		1.3 Solutions
			1.3.1 Helium Dimers and Trimers
			1.3.2 Interferences of Large Material Particles
			1.3.3 References
	2 Neutron Interferometry
		2.1 Neutron Interferences
		2.2 The Gravitational Effect
		2.3 Rotating a Spin 1/2 by 360 Degrees
		2.4 Solutions
			2.4.1 Neutron Interferences
			2.4.2 The Gravitational Effect
			2.4.3 Rotating a Spin 1/2 by 360 Degrees
			2.4.4 References
	3 Analysis of a Stern–Gerlach Experiment
		3.1 Preparation of the Neutron Beam
		3.2 Spin State of the Neutrons
		3.3 The Stern–Gerlach Experiment
		3.4 Solutions
			3.4.1 Preparation of the Neutron Beam
			3.4.2 Spin State of the Neutrons
			3.4.3 The Stern-Gerlach Experiment
	4 Spectroscopic Measurements on a Neutron Beam
		4.1 The Ramsey Method of Separated Oscillatory Fields
		4.2 Solutions
	5 Measuring the Electron Magnetic Moment Anomaly
		5.1 Spin and Momentum Precession in a Magnetic Field
		5.2 Solutions
	6 Atomic Clocks
		6.1 The Hyperfine Splitting of the Ground State
		6.2 The Atomic Fountain
		6.3 The GPS System
		6.4 The Drift of Fundamental Constants
		6.5 Solutions
			6.5.1 Hyperfine Splitting of the Ground State
			6.5.2 The Atomic Fountain
			6.5.3 The GPS System
			6.5.4 The Drift of Fundamental Constants
			6.5.5 References
	7 The Spectrum of Positronium
		7.1 Positronium Orbital States
		7.2 Hyperfine Splitting
		7.3 Zeeman Effect in the Ground State
		7.4 Decay of Positronium
		7.5 Solutions
			7.5.1 Positronium Orbital States
			7.5.2 Hyperfine Splitting
			7.5.3 Zeeman Effect in the Ground State
			7.5.4 Decay of Positronium
			7.5.5 References
	8 Neutrino Transformations in the Sun
		8.1 Neutrino Oscillations in Vacuum
		8.2 Interaction of Neutrinos with Matter
		8.3 Solutions
			8.3.1 Neutrino Oscillations in the Vacuum
			8.3.2 Interaction of Neutrinos with Matter
	9 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
			9.3.1 The Hydrogen Atom in Crossed Electric and Magnetic Fields
			9.3.2 Pauli\'s Result
			9.3.3 References
	10 Energy Loss of Ions in Matter
		10.1 Energy Absorbed by One Atom
		10.2 Energy Loss in Matter
		10.3 Solutions
			10.3.1 Energy Absorbed by One Atom
			10.3.2 Energy Loss in Matter
			10.3.3 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
			11.6.1 The Electron Spin
			11.6.2 Correlations Between the Two Spins
			11.6.3 Correlations in the Singlet State
			11.6.4 A Simple Hidden Variable Model
			11.6.5 Bell\'s Theorem and Experimental Results
			11.6.6 References
	12 Quantum Correlations in a Multi-particle System
		12.1 Measurements on a Single Spin
		12.2 Measurements on a Two-Spin System
		12.3 Measurements on a Four-Spin System
		12.4 Solutions
			12.4.1 Measurements on a Single Spin
			12.4.2 Measurements on a Two-Spin System
			12.4.3 Measurements on a Four-Spin System
			12.4.4 References
	13 A Non-destructive Bomb Detector
		13.1 A Neutron Beam Splitter
		13.2 A Mach–Zehnder Interferometer for Neutrons
		13.3 A First Step Towards a Non Destructive Detection
		13.4 Towards an Efficient Non-destructive Detection
		13.5 Solutions
			13.5.1 A Neutron Beam Splitter
			13.5.2 A Mach-Zehnder Interferometer for Neutrons
			13.5.3 A First Step Towards a Non Destructive Detection
			13.5.4 Towards an Efficient Non-destructive Detection
			13.5.5 References
	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
			14.6.1 Quantization of a Mode of the Electromagnetic Field
			14.6.2 The Coupling of the Field with an Atom
			14.6.3 Interaction of the Atom and an ``Empty\'\' Cavity
			14.6.4 Interaction of an Atom with a Quasi-classical State
			14.6.5 Large Numbers of Photons: Damping and Revivals
			14.6.6 Comments
	15 Schrödinger\'s Cat
		15.1 The Quasi-classical States of a Harmonic Oscillator
		15.2 Construction of a Schrödinger-Cat State
		15.3 Quantum Superposition Versus Statistical Mixture
		15.4 The Fragility of a Quantum Superposition
		15.5 Solutions
			15.5.1 The Quasi-classical States of a Harmonic Oscillator
			15.5.2 Construction of a Schrödinger-Cat State
			15.5.3 Quantum Superposition Versus Statistical Mixture
			15.5.4 The Fragility of a Quantum Superposition
			15.5.5 Comments
	16 Quantum Cryptography
		16.1 Preliminaries
		16.2 Correlated Pairs of Spins
		16.3 The Quantum Cryptography Procedure
		16.4 Solutions
			16.4.1 Preliminaries
			16.4.2 Correlated Pairs of Spins
			16.4.3 The Quantum Cryptography Procedure
			16.4.4 References
	17 Ideal Quantum Measurement
		17.1 A Von Neumann Detector
		17.2 Phase States of the Harmonic Oscillator
		17.3 The Interaction Between the System and the Detector
		17.4 An ``Ideal\'\' Measurement
		17.5 Solutions
			17.5.1 A Von Neumann Detector
			17.5.2 Phase States of the Harmonic Oscillator
			17.5.3 The Interaction Between the System and the Detector
			17.5.4 An ``Ideal\'\' Measurement
			17.5.5 Comments
	18 The Quantum Eraser
		18.1 Magnetic Resonance
		18.2 Ramsey Fringes
		18.3 Detection of the Neutron Spin State
		18.4 A Quantum Eraser
		18.5 Solutions
			18.5.1 Magnetic Resonance
			18.5.2 Ramsey Fringes
			18.5.3 Detection of the Neutron Spin State
			18.5.4 A Quantum Eraser
			18.5.5 Comments
	19 A Quantum Thermometer
		19.1 The Penning Trap in Classical Mechanics
		19.2 The Penning Trap in Quantum Mechanics
		19.3 Coupling of the Cyclotron and Axial Motions
		19.4 A Quantum Thermometer
		19.5 Solutions
			19.5.1 The Penning Trap in Classical Mechanics
			19.5.2 The Penning Trap in Quantum Mechanics
			19.5.3 Coupling of the Cyclotron and Axial Motions
			19.5.4 A Quantum Thermometer
	20 Laser Cooling and Trapping
		20.1 Optical Bloch Equations for an Atom at Rest
		20.2 The Radiation Pressure Force
		20.3 Doppler Cooling
		20.4 The Dipole Force
		20.5 Solutions
			20.5.1 Optical Bloch Equations for an Atom at Rest
			20.5.2 The Radiation Pressure Force
			20.5.3 Doppler Cooling
			20.5.4 The Dipole Force
			20.5.5 Comments and References
Part III Complex Systems
	21 Exact Results for the Three-Body Problem
		21.1 The Two-Body Problem
		21.2 The Variational Method
		21.3 Relating the Three-Body and Two-Body Sectors
		21.4 The Three-Body Harmonic Oscillator
		21.5 From Mesons to Baryons in the Quark Model
		21.6 Solutions
			21.6.1 The Two-Body Problem
			21.6.2 The Variational Method
			21.6.3 Relating the Three-Body and Two-Body Sectors
			21.6.4 The Three-Body Harmonic Oscillator
			21.6.5 From Mesons to Baryons in the Quark Model
			21.6.6 References
	22 Properties of a Bose–Einstein Condensate
		22.1 Particle in a Harmonic Trap
		22.2 Interactions Between Two Confined Particles
		22.3 Energy of a Bose–Einstein Condensate
		22.4 Condensates with Repulsive Interactions
		22.5 Condensates with Attractive Interactions
		22.6 Solutions
			22.6.1 Particle in a Harmonic Trap
			22.6.2 Interactions Between Two Confined Particles
			22.6.3 Energy of a Bose–Einstein Condensate
			22.6.4 Condensates with Repulsive Interactions
			22.6.5 Condensates with Attractive Interactions
			22.6.6 Comments and References
	23 Quantized Vortices
		23.1 Magnetic Trapping
		23.2 The Two-Dimensional Harmonic Oscillator
		23.3 Quantum Physics in a Rotating Frame
		23.4 Nucleation of Quantized Vortices
		23.5 Solutions
			23.5.1 Magnetic Trapping
			23.5.2 The Two-Dimensional Harmonic Oscillator
			23.5.3 Quantum Physics in a Rotating Frame
			23.5.4 Nucleation of Quantized Vortices
			23.5.5 References
	24 Motion in a Periodic Potential and Bloch Oscillations
		24.1 The Two-Site Problem
		24.2 The Infinite Periodic Chain
		24.3 Dynamics Along the Infinite Chain
		24.4 Bloch Oscillations
		24.5 Solutions
			24.5.1 The Two-Site Problem
			24.5.2 The Infinite Periodic Chain
			24.5.3 Dynamics Along the Infinite Chain
			24.5.4 Bloch Oscillations
			24.5.5 Discussion and References
	25 Magnetic Excitons
		25.1 The Molecule CsFeBr3
		25.2 Spin–Spin Interactions in a Chain of Molecules
		25.3 Energy Levels of the Chain
		25.4 Vibrations of the Chain: Excitons
		25.5 Solutions
			25.5.1 The Molecule CsFeBr3
			25.5.2 Spin–Spin Interactions in a Chain of Molecules
			25.5.3 Energy Levels of the Chain
			25.5.4 Vibrations of the Chain: Excitons
	26 A Quantum Box
		26.1 Results on the One-Dimensional Harmonic Oscillator
		26.2 The Quantum Box
		26.3 Quantum Box in a Magnetic Field
		26.4 Experimental Verification
		26.5 Anisotropy of a Quantum Box
		26.6 Solutions
			26.6.1 Results on the One-Dimensional Harmonic Oscillator
			26.6.2 The Quantum Box
			26.6.3 Quantum Box in a Magnetic Field
			26.6.4 Experimental Verification
			26.6.5 Anisotropy of a Quantum Box
			26.6.6 Comments and References
	27 Colored Molecular Ions
		27.1 Hydrocarbon Ions
		27.2 Nitrogenous Ions
		27.3 Solutions
			27.3.1 Hydrocarbon Ions
			27.3.2 Nitrogenous Ions
	28 Hyperfine Structure in Electron Spin Resonance
		28.1 Hyperfine Interaction with One Nucleus
		28.2 Hyperfine Structure with Several Nuclei
		28.3 Experimental Results
		28.4 Solutions
			28.4.1 Hyperfine Interaction with One Nucleus
			28.4.2 Hyperfine Structure with Several Nuclei
			28.4.3 Experimental Results
	29 Probing Matter with Positive Muons
		29.1 Muonium in Vacuum
		29.2 Muonium in Silicon
		29.3 Solutions
			29.3.1 Muonium in Vacuum
			29.3.2 Muonium in Silicon
			29.3.3 References
	30 Quantum Reflection of Atoms from a Surface
		30.1 The Hydrogen Atom–Liquid Helium Interaction
		30.2 Excitations on the Surface of Liquid Helium
		30.3 Quantum Interaction Between H and Liquid He
		30.4 The Sticking Probability
		30.5 Solutions
			30.5.1 The Hydrogen Atom–Liquid Helium Interaction
			30.5.2 Excitations on the Surface of Liquid Helium
			30.5.3 Quantum Interaction Between H and Liquid He
			30.5.4 The Sticking Probability
			30.5.5 Comments and References
Part IV Appendix
	31 Appendix: Memento of Quantum Mechanics
		31.1 Principles
			31.1.1 Hilbert Space
			31.1.2 Definition of the State of a System; Pure Case
			31.1.3 Measurement
			31.1.4 Evolution
			31.1.5 Complete Set of Commuting Observables (CSCO)
			31.1.6 Entangled States
			31.1.7 Statistical Mixture and the Density Operator
		31.2 General Results
			31.2.1 Uncertainty Relations
			31.2.2 Ehrenfest Theorem
		31.3 The Particular Case of a Point-Like Particle; Wave Mechanics
			31.3.1 The Wave Function
			31.3.2 Operators
			31.3.3 Continuity of the Wave Function
			31.3.4 Position-Momentum Uncertainty Relations
		31.4 Angular Momentum and Spin
			31.4.1 Angular Momentum Observable
			31.4.2 Eigenvalues of the Angular Momentum
			31.4.3 Orbital Angular Momentum of a Particle
			31.4.4 Spin
			31.4.5 Addition of Angular Momenta
		31.5 Exactly Soluble Problems
			31.5.1 The Harmonic Oscillator
			31.5.2 The Coulomb Potential (Bound States)
		31.6 Approximation Methods
			31.6.1 Time-Independent Perturbations
			31.6.2 Variational Method for the Ground State
		31.7 Identical Particles
		31.8 Time-Evolution of Systems
			31.8.1 Rabi Oscillation
			31.8.2 Time-Dependent Perturbation Theory
			31.8.3 Fermi\'s Golden Rule and Exponential Decay
		31.9 Collision Processes
			31.9.1 Born Approximation
			31.9.2 Scattering by a Bound State
			31.9.3 General Scattering Theory
			31.9.4 Low Energy Scattering
Author Index
Subject Index