Efnisyfirlit

• Preface
• Why I wrote this book?
• Quantum mechanics or quantum optics?
• Structure of the course
• How to use this book (a message to the student)
• Acknowledgements
• Contents
• 1 The quantum postulates
• 1.1 The scope of quantum mechanics
• 1.2 The Hilbert Space Postulate
• 1.3 Polarization of the photon
• 1.4 Quantum measurements
• 1.4.1 The Measurement Postulate
• 1.4.2 Polarization measurements
• 1.5 Quantum interference and complementarity
• 1.6 Quantum cryptography
• 1.6.1 The BB84 protocol
• 1.6.2 Practical matters in quantum cryptography
• 1.7 Operators in quantum mechanics
• 1.8 Projection operators and unnormalized states
• 1.9 Quantum observables
• 1.9.1 Observable operators
• 1.9.2 Mean value and uncertainty of an observable
• 1.9.3 The uncertainty principle
• 1.10 Quantum evolution
• 1.11 Problems
• 2 Entanglement
• 2.1 Tensor product spaces
• 2.1.1 Tensor product states and entangled states
• 2.1.2 Measurements in tensor product spaces
• 2.1.3 Tensor products of operators
• 2.1.4 Local operators
• 2.2 Local measurements of entangled states
• 2.2.1 Remote state preparation
• 2.2.2 Partial inner product
• 2.2.3 Local measurements and causality
• 2.2.4 Mixed states
• 2.3 Quantum nonlocality
• 2.3.1 Einstein–Podolsky–Rosen paradox
• 2.3.2 The Bell inequality
• 2.3.3 Violation of the Bell inequality
• 2.3.4 Greenberger–Horne–Zeilinger (GHZ) nonlocality
• 2.4 An insight into quantum measurements
• 2.4.1 Von Neumann measurements
• 2.4.2 Decoherence
• 2.4.3 Interpretations of quantum mechanics
• 2.4.4 The superposition tree
• 2.5 Quantum computation
• 2.6 Quantum teleportation and its applications
• 2.6.1 Quantum teleportation
• 2.6.2 Quantum repeater
• 2.7 Problems
• 3 One-dimensional motion
• 3.1 Continuous observables
• 3.2 De Broglie wave
• 3.3 Position and momentum bases
• 3.3.1 Conversion between position and momentum bases
• 3.3.2 Position–momentum uncertainty
• 3.3.3 The original Einstein–Podolsky–Rosen paradox
• 3.4 The free space potential
• 3.5 Time-independent Schrödinger equation
• 3.6 Bound states
• 3.7 Unbound states
• 3.7.1 The single-step potential
• 3.7.2 Quantum tunnelling
• 3.8 Harmonic oscillator
• 3.8.1 Annihilation and creation operators
• 3.8.2 Fock states
• 3.8.3 Coherent states
• 3.9 Heisenberg picture
• 3.9.1 Operator evolution
• 3.9.2 Displacement operator
• 3.9.3 Evolution of probability densities
• 3.10 Transformations of harmonic oscillator states
• 3.10.1 Coherent state as displaced vacuum
• 3.10.2 Phase shift
• 3.10.3 Squeezing
• 3.11 Problems
• 4 Angular momentum
• 4.1 3D motion
• 4.2 Rotationally symmetric potential
• 4.2.1 Spherical coordinates
• 4.2.2 Angular momentum
• 4.3 Angular momentum eigenstates
• 4.3.1 Matrix representation of the angular momentum
• 4.3.2 Wavefunctions of angular momentum eigenstates
• 4.3.3 Spin
• 4.4 The hydrogen atom
• 4.4.1 Radial wavefunctions
• 4.4.2 Energy spectrum and transitions
• 4.4.3 The periodic table
• 4.5 The Bloch sphere
• 4.6 Magnetic moment and magnetic field
• 4.6.1 Angular momentum and magnetic moment
• 4.6.2 Stern–Gerlach apparatus
• 4.6.3 Evolution of magnetic states
• 4.7 Magnetic resonance
• 4.7.1 Rotating basis
• 4.7.2 Evolution under the rotating-wave approximation
• 4.7.3 Pulse area
• 4.7.4 Applications of magnetic resonance
• 4.8 Problems
• 5 Quantum physics of complex systems
• 5.1 The density operator
• 5.1.1 Pure and mixed states
• 5.1.2 Diagonal and off-diagonal elements
• 5.1.3 Evolution
• 5.2 Trace
• 5.3 Partial trace
• 5.4 Density matrix and Bloch vector
• 5.5 Density matrix and magnetic resonance
• 5.5.1 Decoherence
• 5.5.2 Thermalization
• 5.5.3 Relaxation and the Bloch vector
• 5.6 Generalized measurements
• 5.6.1 A realistic detector
• 5.6.2 Positive operator-valued measure (POVM)
• 5.7 Quantum tomography
• 5.7.1 Quantum state tomography
• 5.7.2 Quantum process tomography
• 5.7.3 Quantum detector tomography
• 5.8 Problems
• Appendix A Linear algebra basics
• A.1 Linear spaces
• A.2 Basis and dimension
• A.3 Inner Product
• A.4 Orthonormal Basis
• A.5 Adjoint Space
• A.6 Linear Operators
• A.6.1 Operations with linear operators
• A.6.2 Matrices
• A.6.3 Outer products
• A.7 Adjoint and self-adjoint operators
• A.8 Spectral decomposition
• A.9 Commutators
• A.10 Unitary operators
• A.11 Functions of operators
• Appendix B Probabilities and distributions
• B.1 Expectation value and variance
• B.2 Conditional probabilities
• B.3 Binomial and Poisson distributions
• B.4 Probability densities
• Appendix C Optical polarization tutorial
• C.1 Polarization of light
• C.2 Polarizing beam splitter
• C.3 Waveplates
• Appendix D Dirac delta function and the Fourier transformation
• D.1 Dirac delta function
• D.2 Fourier transformation
• Index