Efnisyfirlit

• Half-title
• Title
• Copyright
• Contents
• Foreword
• Preface
• Acknowledgments
• Addendum for the English edition
• Units and physical constants
• 1 Introduction
• 1.1 The structure of matter
• 1.1.1 Length scales from cosmology to elementary particles
• 1.1.2 States of matter
• 1.1.3 Elementary constituents
• 1.1.4 The fundamental interactions
• 1.2 Classical and quantum physics
• 1.3 A bit of history
• 1.3.1 Black-body radiation
• 1.3.2 The photoelectric effect
• 1.4 Waves and particles: interference
• 1.4.1 The de Broglie hypothesis
• 1.4.2 Diffraction and interference of cold neutrons
• 1.4.3 Interpretation of the experiments
• 1.4.4 Heisenberg inequalities I
• 1.5 Energy levels
• 1.5.1 Energy levels in classical mechanics and classical models of the atom
• 1.5.2 The Bohr atom
• 1.5.3 Orders of magnitude in atomic physics
• 1.6 Exercises
• 1.6.1 Orders of magnitude
• 1.6.2 The black body
• 1.6.3 Heisenberg inequalities
• 1.6.4 Neutron diffraction by a crystal
• 1.6.5 Hydrogen-like atoms
• 1.6.6 The Mach–Zehnder interferometer
• 1.6.7 Neutron interferometry and gravity
• 1.6.8 Coherent and incoherent neutron scattering by a crystal
• 1.7 Further reading
• 2 The mathematics of quantum mechanics I: finite dimension
• 2.1 Hilbert spaces of finite dimension
• 2.2 Linear operators on H
• 2.2.1 Linear, Hermitian, unitary operators
• 2.2.2 Projection operators and Dirac notation
• 2.3 Spectral decomposition of Hermitian operators
• 2.3.1 Diagonalization of a Hermitian operator
• 2.3.2 Diagonalization of a 2×2 Hermitian matrix
• 2.3.3 Complete sets of compatible operators
• 2.3.4 Unitary operators and Hermitian operators
• 2.3.5 Operator-valued functions
• 2.4 Exercises
• 2.4.1 The scalar product and the norm
• 2.4.2 Commutators and traces
• 2.4.3 The determinant and the trace
• 2.4.4 A projector in R3
• 2.4.5 The projection theorem
• 2.4.6 Properties of projectors
• 2.4.7 The Gaussian integral
• 2.4.8 Commutators and a degenerate eigenvalue
• 2.4.9 Normal matrices
• 2.4.10 Positive matrices
• 2.4.11 Operator identities
• 2.4.12 A beam splitter
• 2.5 Further reading
• 3 Polarization: photons and spin-1/2 particles
• 3.1 The polarization of light and photon polarization
• 3.1.1 The polarization of an electromagnetic wave
• 3.1.2 The photon polarization
• 3.1.3 Quantum cryptography
• 3.2 Spin 1/2
• 3.2.1 Angular momentum and magnetic moment in classical physics
• 3.2.2 The Stern–Gerlach experiment and Stern–Gerlach filters
• 3.2.3 Spin states of arbitrary orientation
• 3.2.4 Rotation of spin 1/2
• 3.2.5 Dynamics and time evolution
• 3.3 Exercises
• 3.3.1 Decomposition and recombination of polarizations
• 3.3.2 Elliptical polarization
• 3.3.3 Rotation operator for the photon spin
• 3.3.4 Other solutions of (3.45)
• 3.3.5 Decomposition of a 2×2 matrix
• 3.3.6 Exponentials of Pauli matrices and rotation operators
• 3.3.7 The tensor Epsilonijk
• 3.3.8 A 2 rotation of spin 1/2
• 3.3.9 Neutron scattering by a crystal: spin-1/2 nuclei
• 3.4 Further reading
• 4 Postulates of quantum physics
• 4.1 State vectors and physical properties
• 4.1.1 The superposition principle
• 4.1.2 Physical properties and measurement
• 4.1.3 Heisenberg inequalities II
• 4.2 Time evolution
• 4.2.1 The evolution equation
• 4.2.2 The evolution operator
• 4.2.3 Stationary states
• 4.2.4 The temporal Heisenberg inequality
• 4.2.5 The Schrödinger and Heisenberg pictures
• 4.3 Approximations and modeling
• 4.4 Exercises
• 4.4.1 Dispersion and eigenvectors
• 4.4.2 The variational method
• 4.4.3 The Feynman–Hellmann theorem
• 4.4.4 Time evolution of a two-level system
• 4.4.5 Unstable states
• 4.4.6 The solar neutrino puzzle
• 4.4.7 The Schrödinger and Heisenberg pictures
• 4.4.8 The system of neutral K mesons
• 4.5 Further reading
• 5 Systems with a finite number of levels
• 5.1 Elementary quantum chemistry
• 5.1.1 The ethylene molecule
• 5.1.2 The benzene molecule
• 5.2 Nuclear magnetic resonance (NMR)
• 5.2.1 A spin 1/2 in a periodic magnetic field
• 5.2.2 Rabi oscillations
• 5.2.3 Principles of NMR and MRI
• 5.3 The ammonia molecule
• 5.3.1 The ammonia molecule as a two-level system
• 5.3.2 The molecule in an electric field: the ammonia maser
• 5.3.3 Off-resonance transitions
• 5.4 The two-level atom
• 5.5 Exercises
• 5.5.1 An orthonormal basis of eigenvectors
• 5.5.2 The electric dipole moment of formaldehyde
• 5.5.3 Butadiene
• 5.5.4 Eigenvectors of the Hamiltonian (5.47)
• 5.5.5 The hydrogen molecular ion H+2
• 5.5.6 The rotating-wave approximation in NMR
• 5.6 Further reading
• 6 Entangled states
• 6.1 The tensor product of two vector spaces
• 6.1.1 Definition and properties of the tensor product
• Postulate V
• 6.1.2 A system of two spins 1/2
• 6.2 The state operator (or density operator)
• 6.2.1 Definition and properties
• 6.2.2 The state operator for a two-level system
• 6.2.3 The reduced state operator
• 6.2.4 Time dependence of the state operator
• 6.2.5 General form of the postulates
• 6.3 Examples
• 6.3.1 The EPR argument
• 6.3.2 Bell inequalities
• 6.3.3 Interference and entangled states
• 6.3.4 Three-particle entangled states (GHZ states)
• 6.4 Applications
• 6.4.1 Measurement and decoherence
• 6.4.2 Quantum information
• 6.5 Exercises
• 6.5.1 Independence of the tensor product from the choice of basis
• 6.5.2 The tensor product of two 2×2 matrices
• 6.5.3 Properties of state operators
• 6.5.4 Fine structure and the Zeeman effect in positronium
• 6.5.5 Spin waves and magnons
• 6.5.6 Spin echo and level splitting in NMR
• 6.5.7 Calculation of E(a, b)
• 6.5.8 Bell inequalities involving photons
• 6.5.9 Two-photon interference
• 6.5.10 Interference of emission times
• 6.5.11 The Deutsch algorithm
• 6.6 Further reading
• 7 Mathematics of quantum mechanics II: infinite dimension
• 7.1 Hilbert spaces
• 7.1.1 Definitions
• 7.1.2 Realizations of separable spaces of infinite dimension
• 7.2 Linear operators on H
• 7.2.1 The domain and norm of an operator
• 7.2.2 Hermitian conjugation
• 7.3 Spectral decomposition
• 7.3.1 Hermitian operators
• 7.3.2 Unitary operators
• 7.4 Exercises
• 7.4.1 Spaces of infinite dimension
• 7.4.2 Spectrum of a Hermitian operator
• 7.4.3 Canonical commutation relations
• 7.4.4 Dilatation operators and the conformal transformation
• 7.5 Further reading
• 8 Symmetries in quantum physics
• 8.1 Transformation of a state in a symmetry operation
• 8.1.1 Invariance of probabilities in a symmetry operation
• 8.1.2 The Wigner theorem
• 8.2 Infinitesimal generators
• 8.2.1 Definitions
• 8.2.2 Conservation laws
• 8.2.3 Commutation relations of infinitesimal generators
• 8.3 Canonical commutation relations
• 8.3.1 Dimension d = 1
• 8.3.2 Explicit realization and von Neumann’s theorem
• 8.3.3 The parity operator
• 8.4 Galilean invariance
• 8.4.1 The Hamiltonian in dimension d = 1
• 8.4.2 The Hamiltonian in dimension d = 3
• 8.5 Exercises
• 8.5.1 Rotations
• 8.5.2 Rotations and SU(2)
• 8.5.3 Commutation relations between momentum and angular momentum
• 8.5.4 The Lie algebra of a continuous group
• 8.5.5 The Thomas–Reiche–Kuhn sum rule
• 8.5.6 The center of mass and the reduced mass
• 8.5.7 The Galilean transformation
• 8.6 Further reading
• 9 Wave mechanics
• 9.1 Diagonalization of X and P and wave functions
• 9.1.1 Diagonalization of X
• 9.1.2 Realization in…
• 9.1.3 Realization in…
• 9.1.4 Evolution of a free wave packet
• 9.2 The Schrödinger equation
• 9.2.1 The Hamiltonian of the Schrödinger equation
• 9.2.2 The probability density and the probability current density
• 9.3 Solution of the time-independent Schrödinger equation
• 9.3.1 Generalities
• 9.3.2 Reflection and transmission by a potential step
• The potential step: total reflection
• The potential step: reflection and transmission
• 9.3.3 The bound states of the square well
• 9.4 Potential scattering
• 9.4.1 The transmission matrix
• 9.4.2 The tunnel effect
• 9.4.3 The S matrix
• 9.5 The periodic potential
• 9.5.1 The Bloch theorem
• 9.5.2 Energy bands
• 9.6 Wave mechanics in dimension d = 3
• 9.6.1 Generalities
• 9.6.2 The phase space and level density
• 9.6.3 The Fermi Golden Rule
• 9.7 Exercises
• 9.7.1 The Heisenberg inequalities
• 9.7.2 Wave-packet spreading
• 9.7.3 A Gaussian wave packet
• 9.7.4 Heuristic estimates using the Heisenberg inequality
• 9.7.5 The Lennard–Jones potential for helium
• 9.7.6 Reflection delay
• 9.7.7 A delta-function potential
• 9.7.8 Transmission by a well
• 9.7.9 Energy levels of an infinite cubic well in dimension d = 3
• 9.7.10 The probability current in three dimensions
• 9.7.11 The level density
• 9.7.12 The Fermi Golden Rule
• 9.7.13 Study of the Stern–Gerlach experiment
• 9.7.14 The von Neumann model of measurement
• 9.7.15 The Galilean transformation
• 9.8 Further reading
• 10 Angular momentum
• 10.1 Diagonalization of J2 and Jz
• 10.2 Rotation matrices
• 10.3 Orbital angular momentum
• 10.3.1 The orbital angular momentum operator
• 10.3.2 Properties of the spherical harmonics
• 1. Basis on the unit sphere
• 2. Relation to the Legendre polynomials
• 3. Transformation under rotation
• 4. Parity of the spherical harmonics
• 10.4 Particle in a central potential
• 10.4.1 The radial wave equation
• 10.4.2 The hydrogen atom
• 10.5 Angular distributions in decays
• 10.5.1 Rotations by pi, parity, and reflection with respect to a plane
• 10.5.2 Dipole transitions
• 10.5.3 Two-body decays: the general case
• 10.6 Addition of two angular momenta
• 10.6.1 Addition of two spins 1/2
• 10.6.2 The general case: addition of two angular momenta J1 and J2
• 10.6.3 Composition of rotation matrices
• 10.6.4 The Wigner–Eckart theorem (scalar and vector operators)
• 10.7 Exercises
• 10.7.1 Properties of J
• 10.7.2 Rotation of angular momentum
• 10.7.3 Rotations (theta, phi)
• 10.7.4 The angular momenta…
• 10.7.5 Orbital angular momentum
• 10.7.6 Relation between the rotation matrices and the spherical harmonics
• 10.7.7 Independence of the energy from m
• 10.7.8 The spherical well
• 10.7.9 The hydrogen atom for…
• 10.7.10 Matrix elements of a potential
• 10.7.11 The radial equation in dimension d = 2
• 10.7.12 Symmetry property of the matrices d(j)
• 10.7.13 Light scattering
• 10.7.14 Measurement of the Lambda0 magnetic moment
• 10.7.15 Production and decay of the rho+ meson
• 10.7.16 Interaction of two dipoles
• 10.7.17 Sigma0 decay
• 10.7.18 Irreducible tensor operators
• 10.8 Further reading
• 11 The harmonic oscillator
• 11.1 The simple harmonic oscillator
• 11.1.1 Creation and annihilation operators
• 11.1.2 Diagonalization of the Hamiltonian
• 11.1.3 Wave functions of the harmonic oscillator
• 11.2 Coherent states
• 11.3 Introduction to quantized fields
• 11.3.1 Sound waves and phonons
• 11.3.2 Quantization of a scalar field in one dimension
• 11.3.3 Quantization of the electromagnetic field
• 11.3.4 Quantum fluctuations of the electromagnetic field
• 11.4 Motion in a magnetic field
• 11.4.1 Local gauge invariance
• 11.4.2 A uniform magnetic field: Landau levels
• 11.5 Exercises
• 11.5.1 Matrix elements of Q and P
• 11.5.2 Mathematical properties
• 11.5.3 Coherent states
• 11.5.4 Coupling to a classical force
• 11.5.5 Squeezed states
• 11.5.6 Zero-point energy of the Debye model
• 11.5.7 The scalar and vector potentials in Coulomb gauge
• 11.5.8 Commutation relations and Hamiltonian of the electromagnetic field
• 11.5.9 Quantization in a cavity
• 11.5.10 Current conservation in the presence of a magnetic field
• 11.5.11 Non-Abelian gauge transformations
• 11.5.12 The Casimir effect
• 11.5.13 Quantum computing with trapped ions
• 11.6 Further reading
• 12 Elementary scattering theory
• 12.1 The cross section and scattering amplitude
• 12.1.1 The differential and total cross sections
• 12.1.2 The scattering amplitude
• 12.2 Partial waves and phase shifts
• 12.2.1 The partial-wave expansion
• 12.2.2 Low-energy scattering
• 12.2.3 The effective potential
• 12.2.4 Low-energy neutron–proton scattering
• 12.3 Inelastic scattering
• 12.3.1 The optical theorem
• 12.3.2 The optical potential
• 12.4 Formal aspects
• 12.4.1 The integral equation of scattering
• 12.4.2 Scattering of a wave packet
• 12.5 Exercises
• 12.5.1 The Gamow peak
• 12.5.2 Low-energy neutron scattering by a hydrogen molecule
• 12.5.3 Analytic properties of the neutron–proton scattering amplitude
• 12.5.4 The Born approximation
• 12.5.5 Neutron optics
• 12.5.6 The cross section for neutrino absorption
• 12.6 Further reading
• 13 Identical particles
• 13.1 Bosons and fermions
• 13.1.1 Symmetry or antisymmetry of the state vector
• 13.1.2 Spin and statistics
• 13.2 The scattering of identical particles
• 13.3 Collective states
• 13.4 Exercises
• 13.4.1 The Tonos- particle and color
• 13.4.2 Parity of the pi meson
• 13.4.3 Spin-1/2 fermions in an infinite well
• 13.4.4 Positronium decay
• 13.4.5 Quantum statistics and beam splitters
• 13.5 Further reading
• 14 Atomic physics
• 14.1 Approximation methods
• 14.1.1 Generalities
• 14.1.2 Nondegenerate perturbation theory
• 14.1.3 Degenerate perturbation theory
• 14.1.4 The variational method
• 14.2 One-electron atoms
• 14.2.1 Energy levels in the absence of spin
• 14.2.2 The fine structure
• 14.2.3 The Zeeman effect
• 14.2.4 The hyperfine structure
• 14.3 Atomic interactions with an electromagnetic field
• 14.3.1 The semiclassical theory
• 14.3.2 The dipole approximation
• 14.3.3 The photoelectric effect
• 14.3.4 The quantized electromagnetic field: spontaneous emission
• 14.4 Laser cooling and trapping of atoms
• 14.4.1 The optical Bloch equations
• 14.4.2 Dissipative forces and reactive forces
• 14.4.3 Doppler cooling
• 14.4.4 A magneto-optical trap
• 14.5 The two-electron atom
• 14.5.1 The ground state of the helium atom
• 14.5.2 The excited states of the helium atom
• 14.6 Exercises
• 14.6.1 Second-order perturbation theory and van der Waals forces
• 14.6.2 Order-alpha2 corrections to the energy levels
• 14.6.3 Muonic atoms
• 14.6.4 Rydberg atoms
• 14.6.5 The diamagnetic term
• 14.6.6 Vacuum Rabi oscillations
• 14.6.7 Reactive forces
• 14.6.8 Radiative capture of neutrons by hydrogen
• 14.7 Further reading
• 15 Open quantum systems
• 15.1 Generalized measurements
• 15.1.1 Schmidt’s decomposition
• 15.1.2 Positive operator-valued measures
• 15.1.3 Example: a POVM with spins 1/2
• 15.2 Superoperators
• 15.2.1 Kraus decomposition
• 15.2.2 The depolarizing channel
• 15.2.3 The phase-damping channel
• 15.2.4 The amplitude-damping channel
• 15.3 Master equations: the Lindblad form
• 15.3.1 The Markovian approximation
• 15.3.2 The Lindblad equation
• 15.3.3 Example: the damped harmonic oscillator
• 15.4 Coupling to a thermal bath of oscillators
• 15.4.1 Exact evolution equations
• 15.4.2 The Markovian approximation
• 15.4.3 Relaxation of a two-level system
• 15.4.4 Quantum Brownian motion
• 15.4.5 Decoherence and Schrödinger’s cats
• 15.5 Exercises
• 15.5.1 POVM as projective measurement in a direct sum
• 15.5.2 Using a POVM to distinguish between states
• 15.5.3 A POVM on two arbitrary qubit states
• 15.5.4 Transposition is not completely positive
• 15.5.5 Phase and amplitude damping
• 15.5.6 Details of the proof of the master equation
• 15.5.7 Superposition of coherent states
• 15.5.8 Dissipation in a two-level system
• 15.5.9 Simple models of relaxation
• 15.5.10 Another choice for the spectral function J(omega)
• 15.5.11 The Fokker–Planck–Kramers equation for a Brownian particle
• 15.6 Further reading
• Appendix A The Wigner theorem and time reversal
• A.1 Proof of the theorem
• A.2 Time reversal
• Appendix B Measurement and decoherence
• B.1 An elementary model of measurement
• B.2 Ramsey fringes
• B.3 Interaction with a field inside the cavity
• B.4 Decoherence
• Appendix C The Wigner–Weisskopf method
• References
• Index