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

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