دانلود کتاب Quantum Physics: The Bottom-Up Approach: From the Simple Two-Level System to Irreducible Representations

This concise tutorial provides the bachelor student and the practitioner with a short text on quantum physics that allows them to understand a wealth of quantum phenomena based on a compact, well readable, yet still concise and accurate description of nonrelativistic quantum theory. This “quadrature of the circle” is achieved by concentrating first on the simplest quantum system that still displays all basic features of quantum theory, namely, a system with only two quantized energy levels. For most readers it is very helpful to understand such simple systems before slowly proceeding to more demanding topics like particle entanglement, quantum chaos, or the use of irreducible tensors. This tutorial does not intend to replace the standard textbooks on quantum mechanics, but will help the average student to understand them, often for the first time.

Table of Contents

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Quantum Physics: The Bottom-Up Approach - From the Simple Two-Level System to Irreducible Representations

ISBN 9783642310591 ISBN 9783642310607

Preface

Contents

Part I Prologue

Chapter 1 Recollections from Elementary Quantum Physics

Part II Two-State Quantum Systems

Chapter 2 A Most Simple Two-Level System
2.1 Magnetic Moment and Spin
2.2 Zeeman Effect
2.3 Stern-Gerlach Effect
Chapter 3 Quantum Theory in a Nutshell
3.1 Spin Matrices
3.2 Energy Matrices
3.3 Expectation Values
o 3.3.1 Expectation Value of Energy
o 3.3.2 Expectation Value of Spin
3.4 Uncertainties
o 3.4.1 Uncertainty of Spin
o 3.4.2 Uncertainty of Energy
3.5 Spin Precession
o 3.5.1 Longitudinal Field
o 3.5.2 Transverse Field
Chapter 4 Experiments on Spin Precession
4.1 Muon Spin Precession
4.2 Light Scattering
4.3 Spinor Rotation Through 720�
Chapter 5 General Solution for the Two-Level System
5.1 Matrix Diagonalization
5.2 Construction of the Eigenvectors
5.3 The Time Dependent Solution
o 5.3.1 Evolution of an Energy Eigenstate
o 5.3.2 Evolution of an Angular-Momentum Eigenstate
Chapter 6 Other Tools and Concepts
6.1 Time Evolution Operator
6.2 Rotation Matrices
6.3 Projection Operators
6.4 Pure States and Mixed States
6.5 The Density Matrix
6.6 Coherence and Interference
6.7 Dirac's Bra-Ket Notation
Chapter 7 Diabolic Points, Geometric Phases, and Quantum Chaos
7.1 Level Crossings and Level Repulsions
o 7.1.1 The Field Dependence of Energy and of Polarization
o 7.1.2 Level Repulsion in a Spin1
o 7.1.3 Level Repulsion in a Spin-1 System
7.2 The Adiabatic Theorem
7.3 Geometric Phases
o 7.3.1 Derivation of the Berry Phase
o 7.3.2 Excursions in Magnetic-Field Space
o 7.3.3 Excursions in the Space of Shapes
o 7.3.4 The Aharonov-Bohm Effect
7.4 Quantum Chaos
Chapter 8 The Coupling of Particles
8.1 Bosons and Fermions
8.2 The Coupling of Spins
8.3 Example: Hyperfin Structure
Chapter 9 "Spooky Action at a Distance"
9.1 Quantum Entanglement
9.2 Bell's Inequalities
Chapter 10 The Heisenberg Equation of Motion
10.1 Matrix Mechanics
10.2 Commutation Relations and Uncertainty Principle
10.3 The Bloch Equations

Part III Quantum Physics at Work

Chapter 11 Spin Resonance
11.1 Basics of Spin Resonance
11.2 Methods of Spin Resonance
11.3 Applications of Spin Resonance
Chapter 12 Two-State Systems in Atomic and Molecular Physics
12.1 Photons as Two-State Systems
12.2 Optical Resonance Transitions
12.3 Optical Analogies of Spin Rotation and Spin Resonance
12.4 Particles in a Double Well
o 12.4.1 The NH3 Molecule
o 12.4.2 The Ammonia Maser
o 12.4.3 Bose-Einstein Condensate in a Double Trap
Chapter 13 Two-State Systems in Condensed Matter
13.1 Glasses
13.2 Josephson Effects
o 13.2.1 Basics of Superconductivity
o 13.2.2 Josephson Junctions and Their Applications
Chapter 14 Two-State Systems in Nuclear and Particle Physics
14.1 Isospin
14.2 Flavor and Color
14.3 Particle Oscillations
o 14.3.1 Kaon Oscillations
o 14.3.2 Neutrino Oscillations
o 14.3.3 Neutron Oscillations
Chapter 15 Quantum Informatics
15.1 Quantum Information Theory
15.2 Quantum Computing and Quantum Communication

Part IV Multilevel Systems and Tensor Operators

Chapter 16 Rotations and Angular Momentum
16.1 Symmetries
16.2 Properties of Angular Momentum
16.3 Representations
16.4 The Spherical Harmonics
16.5 The Rotation Matrices
Chapter 17 Irreducible Tensors
17.1 Scalars, Vectors, and Tensors
17.2 Properties of Irreducible Tensors
o 17.2.1 Definition of Irreducible Tensors
o 17.2.2 A More Practical Definitio
o 17.2.3 Simple Examples
17.3 The Coupling of Irreducible Tensors
o 17.3.1 The Coupling of Angular Momenta
o 17.3.2 General Tensor Coupling
o 17.3.3 Some Special Cases
17.4 The Wigner-Eckart Theorem
Chapter 18 Electromagnetic Multipole Interactions
18.1 Static Magnetic Interactions
18.2 Static Electric Interactions
o 18.2.1 Multipole Expansion of Electrostatic Energy
o 18.2.2 Electric Quadrupole Interaction
18.3 Selection Rules for Electromagnetic Transitions
Chapter 19 The Generalized Spin Precession Equation
19.1 The Density Matrix
o 19.1.1 Definition of the Density Matrix
o 19.1.2 The Liouville Equation of Motion
19.2 Some Preparative Steps
o 19.2.1 Normalized Irreducible Tensor Operators
o 19.2.2 A Bra-Ket Notation for Tensor Operators
19.3 The Irreducible Components of the Density Matrix
o 19.3.1 Definition of the Statistical Tensors
o 19.3.2 Simple Examples of Statistical Tensors
19.4 The Liouville Equation for the Statistical Tensors
Chapter 20 Reorientation in Static Electromagnetic Fields
20.1 Magnetic Dipole Precession
20.2 Electric Quadrupole Reorientation
20.3 Reorientation in Mixed Magnetic and Electric Fields
20.4 Time Average Results
20.5 Angular Distribution of Radiation
o 20.5.1 Asymmetric �-Decay
o 20.5.2 Anisotropic Photon Emission
Chapter 21 Reorientation in Time Dependent Fields
21.1 Radiofrequency Irradiation in a Magnetic Field
o 21.1.1 Density Operator in the Rotating Frame
o 21.1.2 Rotating Wave Approximation
o 21.1.3 Statistical Tensors in the Rotating Wave Approximation
o 21.1.4 Time Average Results
21.2 Multiple Quantum Transitions
21.3 Dressed Atoms
o 21.3.1 Dressed Atoms and the Floquet Theorem
o 21.3.2 Dressed Atoms and Second Quantization
o 21.3.3 A Dressed Neutron Experiment
o 21.3.4 Outlook on Nonclassical Photon Interactions
Chapter 22 Relaxation and Decoherence
22.1 General Features
22.2 The Perturbative Approach
22.3 The Stochastic Approach
22.4 Decoherence

Appendices

Index