1 
Central concepts in classical mechanics 
page 1 

1.1 
Classical description 



1.1.1 
Conservation laws 



1.1.2 
Singleparticle motion for simple potentials 


1.2 
Statistical description of particles 



1.2.1 
Liouville equation 



1.2.2 
Classical averaging of statistical distributions 


Exercises 

2 
Central concepts of classical electrodynamics 
page 26 

2.1 
Classical description of electromagnetic fields 



2.1.1 
Wave equation 



2.1.2 
Superposition of waves 


2.2 
Particle aspects of electromagnetic waves 



2.2.1 
Eikonal equation 



2.2.2 
Classical trajectories within wave equation 


2.3 
Generalized wave and Helmholtz equations 



2.3.1 
Formal eigenvalue problem 



2.3.2 
Temporal properties of generalized waves 



2.3.3 
Generalized waves and particles 


Exercises 

3 
Central concepts in quantum mechanics 
page 48 

3.1 
Schrödinger equation 



3.1.1 
Free quantummechanical propagation 



3.1.2 
Interpretation of the wave function 


3.2 
Expectation values in quantum mechanics 



3.2.1 
Particle momentum 



3.2.2 
Commutation relations 



3.2.3 
Canonical quantization 



3.2.4 
Representations of position and momentum operators 


Exercises 

4 
Central concepts in stationary quantum theory 
page 65 

4.1 
Stationary Schrödinger equation 


4.2 
Onedimensional Schrödinger equation 


4.3 
Classification of stationary eigenstates 



4.3.1 
Propagating solutions 



4.3.2 
Tunneling solutions 



4.3.3 
Bound solutions 


4.4 
Generic classification of energy eigenstates 


Exercises 

5 
Central concepts in measurement theory 
page 86 

5.1 
Hermitian operators 


5.2 
Eigenvalue problems 



5.2.1 
Dirac notation 



5.2.2 
Central eigenvalue problems 


5.3 
Born's theorem 



5.3.1 
Heisenberg uncertainty principle 



5.3.2 
Schrödinger and Heisenberg picture 


Exercises 

6 
Wigner's phasespace representation 
page 101 

6.1 
Wigner function 



6.1.1 
Averages in phase space 



6.1.2 
Quantum properties of the Wigner function 



6.1.3 
Negativity of the Wigner function 


6.2 
Wignerfunction dynamics 


6.3 
Density matrix 


6.4 
Feasibility of quantumdynamical computations 


Exercises 

7 
Hamiltonian formulation of classical electrodynamics 
page 121 

7.1 
Basic concepts 


7.2 
Hamiltonian for classical electrodynamics 



7.2.1 
Functional derivative 



7.2.2 
Electromagneticfield Hamiltonian 


7.3 
Hamilton equations for lightmatter system 



7.3.1 
Classical particle equations 



7.3.2 
Classical equations for the
electromagnetic field 


7.4 
Generalized system Hamiltonian 


Exercises 

8 
System Hamiltonian of classical electrodynamics 
page 141 

8.1 
Elimination of the scalar potential 


8.2 
Coulomb and Lorentz gauge 



8.2.1 
Scalarpotential elimination in the
Coulomb gauge 



8.2.2 
Scalarpotential elimination in the
Lorentz gauge 


8.3 
Transversal and longitudinal fields 



8.3.1 
Poisson equation 



8.3.2 
Wave equation 


8.4 
Mode expansion of the electromagnetic field 



8.4.1 
Modes with periodic boundary conditions 



8.4.2 
Realvalued mode expansion 



8.4.3 
Particle aspects 


Exercises 

9 
System Hamiltonian in the generalized Coulomb gauge 
page 162 

9.1 
Separation of electronic and ionic motion 


9.2 
Inclusion of the ionic polarizability 



9.2.1 
Generalized Coulomb gauge 



9.2.2 
System Hamiltonian 


9.3 
Generalized Coulomb potential 



9.3.1 
Image potentials 



9.3.2 
Generalized Coulomb potential 


9.4 
Generalized lightmode functions 



9.4.1 
Transmission and reflection of light modes 



9.4.2 
Boundary conditions 



9.4.3 
Fresnel coefficients for s and ppolarized modes 



9.4.4 
Transfermatrix
solutions for generalized modes 


Exercises 

10 
Quantization of light and matter 
page 193 

10.1 
Canonical quantization 



10.1.1 
Toward semiconductor quantum optics 



10.1.2 
Real vs. auxiliary quantization space 


10.2 
Second quantization of light 



10.2.1 
Unitary transformations 



10.2.2 
Complexvalued modes 


10.3 
Eigenstates of quantized modes 



10.3.1 
Explicit representation of operators 



10.3.2 
Properties of creation and annihilation operators 



10.3.3 
Fock states 



10.3.4 
Fock states in x space 


10.4 
Elementary properties of Fock states 



10.4.1 
Quantum statistics in terms of Fock states 



10.4.2 
Vacuumfield fluctuations 


Exercises 

11 
Quasiparticles in semiconductors 
page 218 

11.1 
Secondquantization formalism 



11.1.1 
Fermion manybody states 



11.1.2 
Fermion creation and annihilation operators 



11.1.3 
Fermions in second quantization 



11.1.4 
Pragmatic formulation of second quantization 


11.2 
System Hamiltonian of solids 



11.2.1 
Second quantization of system Hamiltonian 



11.2.2 
Second quantization of lattice vibrations 


Exercises 

12 
Band structure of solids 
page 240 

12.1 
Electrons in the periodic lattice potential 



12.1.1 
k·p theory 



12.1.2 
Twoband approximation 


12.2 
Systems with reduced effective dimensionality 



12.2.1 
Quasi two, one, and zerodimensional
systems 



12.2.2 
Electron density of states 


Exercises 

13 
Interactions in semiconductors 
page 253 

13.1 
Manybody Hamiltonian 


13.2 
Lightmatter interaction 



13.2.1 
Separation of length scales 



13.2.2 
Lightmattercoupling integrals 



13.2.3 
Inner products within k·p theory 



13.2.4 
Lightmatter interaction in k·p theory 


13.3 
Phononcarrier interaction 


13.4 
Coulomb interaction 


13.5 
Complete system Hamiltonian in different dimensions 



13.5.1 
Quantumwell system Hamiltonian 



13.5.2 
Quantumwire system Hamiltonian 



13.5.3 
Quantumdot system Hamiltonian 


Exercises 

14 
Generic quantum dynamics 
page 279 

14.1 
Dynamics of elementary operators 



14.1.1 
Evaluation strategy 



14.1.2 
Quantum dynamics of free quasiparticles 



14.1.3 
Photonoperator dynamics 



14.1.4 
Macroscopic matterresponse operators 



14.1.5 
Phonon and carrier dynamics 


14.2 
Formal properties of light 



14.2.1 
Quantized wave equation 



14.2.2 
Plasmon response 


14.3 
Formal properties of general operators 



14.3.1 
Operator hierarchy problem 



14.3.2 
BBGKY hierarchy problem 


Exercises 

15 
Clusterexpansion representation of the quantum dynamics 
page 304 

15.1 
Singlet factorization 



15.1.1 
Expectation values of a Slaterdeterminant
state 



15.1.2 
HartreeFock approximation and singlet
factorization 


15.2 
Cluster expansion 



15.2.1 
Boson and Fermion factorizations 



15.2.2 
Most relevant singletdoublet
factorizations 


15.3 
Quantum dynamics of expectation values 


15.4 
Quantum dynamics of correlations 


15.5 
Scattering in terms of correlations 


Exercises 

16 
Simple manybody systems 
page 324 

16.1 
Single pair state 



16.1.1 
Electronhole system 



16.1.2 
Separation of relative and centerofmass
motion 


16.2 
Hydrogenlike eigenstates 



16.2.1 
Lowdimensional systems 



16.2.2 
Numerical solutions of bound and unbound
states 


16.3 
Optical dipole 



16.3.1 
Momentummatrix elements 



16.3.2 
Longwave length limit for the A.p interaction 


Exercises 

17 
Hierarchy problem for dipole systems 
page 345 

17.1 
Quantum dynamics in the A.p picture 



17.1.1 
Lorentz force 



17.1.2 
Time scale for the centerofmass motion 


17.2 
Lightmatter coupling 


17.3 
Dipole emission 



17.3.1 
Dipoleemission dynamics 



17.3.2 
Emission of planar dipoles 


17.4 
Quantum dynamics in the E.x picture 



17.4.1 
GöppertMayer transformation 



17.4.2 
Dipole self energy 



17.4.3 
System Hamiltonian 



17.4.4 
Quantum dynamics 


Exercises 

18 
Twolevel approximation for optical transitions 
page 365 

18.1 
Classical optics in atomic systems 



18.1.1 
Separation of relative and centerofmass
motion 



18.1.2 
Formal aspects of the optical excitation 



18.1.3 
Twolevel approximation 



18.1.4 
Rotatingwave approximation (RWA) 


18.2 
Twolevel system solutions 



18.2.1 
Analytic solution of the twolevel system 



18.2.2 
Blochvector representation 



18.2.3 
Rabi oscillations 



18.2.4 
Pulse area and Rabi flopping 



18.2.5 
Squarepulse excitation 


Exercises 

19 
Selfconsistent extension of the twolevel approach 
page 388 

19.1 
Spatial coupling between light and twolevel system 



19.1.1 
Centerofmass distribution in optical
coupling 



19.1.2 
Optical Bloch equations 



19.1.3 
Angle parameterization of Bloch vector 


19.2 
Maxwelloptical Bloch equations 



19.2.1 
Radiative decay of the atomic dipole 



19.2.2 
Radiative decay of planar dipoles 


19.3 
Optical Bloch equations with radiative coupling 


Exercises 

20 
Dissipative extension of the twolevel approach  page 405 

20.1 
Spin representation of optical excitations 


20.2 
Dynamics of Pauli spin matrices 


20.3 
Phenomenological dephasing 



20.3.1 
Dephasinginduced effects 



20.3.2 
Dephasing and radiative decay 


20.4 
Coupling between reservoir and twolevel system 



20.4.1 
Masterequation description of dephasing 



20.4.2 
Masterequation for twolevel system 


Exercises 

21 
Quantumoptical extension of the twolevel approach 
page 420 

21.1 
Quantumoptical system Hamiltonian 



21.1.1 
Reduction to twolevel system 



21.1.2 
Rotatingwave approximation 



21.1.3 
Operator dynamics 



21.1.4 
Quantumoptical hierarchy problem 


21.2 
JaynesCummings model 



21.2.1 
Eigenstates 



21.2.2 
Interacting JaynesCummings states 



21.2.3 
JaynesCummings ladder 


Exercises 

22 
Quantum dynamics of twolevel system 
page 438 

22.1 
Formal quantum dynamics 



22.1.1 
Wavefunction dynamics 



22.1.2 
Dynamics of density matrices 


22.2 
Quantum Rabi flopping 



22.2.1 
Observation of quantum rungs 



22.2.2 
Semiclassical interpretation 


22.3 
Coherent states 



22.3.1 
Displacement operator 



22.3.2 
Shotnoise limit 


22.4 
Quantumoptical response to superposition states 



22.4.1 
Collapses and revivals of excitations 



22.4.2 
Origin of collapses and revivals 



22.4.3 
Quantumstatistical modifications 


Exercises 

23 
Spectroscopy and quantumoptical correlations 
page 457 

23.1 
Quantumoptical spectroscopy 


23.2 
Quantumstatistical representations 



23.2.1 
Wigner function 



23.2.2 
Quantumstatistical pluralism 


23.3 
Thermal state 



23.3.1 
Thermal fluctuations 



23.3.2 
Quantumoptical spectroscopy with thermal source 


23.4 
Clusterexpansion dynamics 



23.4.1 
Identification of correlated clusters 



23.4.2 
Beyond Maxwelloptical Bloch equations 



23.4.3 
General singletdoublet dynamics 



23.4.4 
Luminescence equations for twolevel system 


23.5 
Quantumoptics at the singletdoublet level 


Exercises 

24 
General aspects of semiconductor optics 
page 480 

24.1 
Semiconductor nanostructures 



24.1.1 
Homogeneous manybody states 



24.1.2 
Twoband model and electronhole picture 


24.2 
Operator dynamics of solids in optical regime 



24.2.1 
Dynamics of elementary operators 



24.2.2 
Explicit operator dynamics 


24.3 
Clusterexpansion dynamics 


24.4 
Relevant singlets and doublets 


24.5 
Dynamics of singlets 



24.5.1 
Separation of singlets and doublets 



24.5.2 
Closed set of singlets 


Exercises 

25 
Introductory semiconductor optics 
page 499 

25.1 
Optical Bloch equations 



25.1.1 
Twolevel aspects of semiconductors 



25.1.2 
Electronic wave function in the singlet
analysis 


25.2 
Linear response 



25.2.1 
Linear polarization 



25.2.2 
Weak excitation of densities 



25.2.3 
Weak squarepulse excitation 



25.2.4 
Transient polarization vs. stationary density 


25.3 
Coherent vs. incoherent quantities 



25.3.1 
Coherent vs. incoherent correlations 



25.3.2 
Coherence in quantum optics 


25.4 
Temporal aspects in semiconductor excitations 



25.4.1 
Rotatingwave approximation 



25.4.2 
Separation of time scales 



25.4.3 
Electrical field and dipole interaction 


Exercises 

26 
Maxwellsemiconductor Bloch equations 
page 521 

26.1 
Semiconductor Bloch equations 



26.1.1 
Maxwellsemiconductor Bloch equations 



26.1.2 
Coupling to doubletcorrelations 


26.2 
Excitonic states 



26.2.1 
Left and righthanded excitonic states 



26.2.2 
Densitydependent aspects of the 1s resonance 


26.3 
Semiconductor Bloch equations in the exciton basis 


26.4 
Linear optical response 



26.4.1 
Elliott formula 



26.4.2 
Selfconsistent optical response 



26.4.3 
Quantitative measurements and dephasing 



26.4.4 
Radiative polarization decay 


26.5 
Excitationinduced dephasing 



26.5.1 
Densitydependent absorption 



26.5.2 
Diffusive model 


Exercises 

27 
Coherent vs. incoherent excitons 
page 550 

27.1 
General singlet excitations 



27.1.1 
Coherent limit 



27.1.2 
Manybody state of singlet excitations 



27.1.3 
Coherent excitonic polarization 


27.2 
Incoherent excitons 



27.2.1 
Dynamics of exciton correlations 



27.2.2 
Polarizationtopopulation transfer 


27.3 
Electronhole correlations in the exciton basis 



27.3.1 
Correlated electronhole plasma 



27.3.2 
Energy considerations 


Exercises 

28 
Semiconductor luminescence equations 
page 572 

28.1 
Incoherent photon emission 



28.1.1 
Photon emission vs. electronhole
recombination 



28.1.2 
Excitoncorrelation dynamics 


28.2 
Dynamics of photonassisted correlations 



28.2.1 
Spontaneousemission source 



28.2.2 
Semiconductor luminescence equations 


28.3 
Analytic investigation of the semiconductor luminescence 



28.3.1 
Wannier excitons with finite centerofmass
momentum 



28.3.2 
Elliott formula for luminescence 



28.3.3 
Plasma vs. population source
in photoluminescence 


28.4 
Excitonic signatures in the semiconductor luminescence 


Exercises 

29 
Manybody aspects of the semiconductor luminescence 
page 593 

29.1 
Origin of excitonic plasma luminescence 



29.1.1 
Energy redistribution dynamics 



29.1.2 
Energy flow between manybody states and
photons 


29.2 
Excitonic plasma luminescence 



29.2.1 
Radiative recombination of carriers vs. excitons 



29.2.2 
Hole burning in exciton distributions 


29.3 
Direct detection of excitons 


Exercises 

30 
Advanced semiconductor quantum optics 
page 608 

30.1 
General singletdoublet dynamics 



30.1.1 
Coherent coupling in the Π^{v,c} dynamics 



30.1.2 
General Π^{λ,λ'} dynamics 



30.1.3 
General dynamics of carrier doublets 



30.1.4 
Singletdoublet correlations and beyond 


30.2 
Advanced quantum optics in the incoherent regime 



30.2.1 
Semiconductor luminescence in a cavity 



30.2.2 
Interference effects in incoherent
luminescence 



30.2.3 
Phonon sidebands 



30.2.4 
Quantumdot emission 


30.3 
Advanced quantum optics in the coherent regime 



30.3.1 
Squeezing in the resonance fluorescence 



30.3.2 
Coherent quantumoptical correlations 



30.3.3 
Quantumoptical spectroscopy 



30.3.4 
Quantum optics in simple vs. complicated
systems 


Exercises 



Appendix  Conservation laws for the transfer matrix 
page 627 

A.1 
Wronskian induced constraints 


A.2 
Current induced constraints 


A.3 
Explicit conservation laws 


Index 
page 633 