Contents of the book by

Ravinder R Puri
Mathematical methods of quantum optics
Springer, Heidelberg (2001)

1.  Basic quantum mechanics .................................  1
Postulates of quantum mechanics
Geometric phase
Time-dependent approximation method
Quantum mechanics of composite system
Quantum mechanics of subsystem and density operator
Systems of one and two spin 1/2 
Wave-particle duality
Measurement postulate and paradoxes of quantum theory
Local hidden variables theory

2.  Algebra of the exponential operator ....................  37
Parametric differentiation of the exponential
Exponential of a finite-dimensional operator
Lie algebraic similarity transformations
Disentagling an exponential
Time-ordered exponential integral

3.  Representations of some Lie algebras ...................  55
Representation by eigenvectors
Representation of harmonic oscillator algebra
Representations of SU(2)
Representations of SU(1,1)

4.  Quasiprobabilities and non-classical states ............  81
Phase-space distribution functions
Phase-space representations of spins
Quasiprobability distributions for eigenvalues of spin components
Classical and non-classical states

5.  Theory of stochastic processes .........................  99
Probability distributions
Markov processes
Detailed balance
Liouville and Fokker-Planck equations
Stochastic differential equations
Linear equations with additive noise
Linear equations with multiplicative noise
The Poisson process

6.  The electromagnetic field .............................. 119
Free classical field
Field quantisation
Statistical properties of classical field
Statistical properties of quantised field
Homodyned detection
Spectrum

7.  Atom-field interaction Hamiltonians .................... 137
Dipole interaction
Rotating wave resonance approximation
Two-level atom
Three-level atom
Effective two-level atom
Mutli-channel models
Parametric processes
Cavity QED
Moving atom

8.  Quantum theory of dampling ............................. 155
The master equation
Solving the master equation
Multi-time average of system operators
Bath of harmonic oscillators
Master equation for a harmonic oscillator
Master equation for a two-level atom
Master equation for a three-level atom

9. Linear and nonlinear response of a system in an external field . 177
Steady state of a system in an external field
Optical susceptibility
Rate of absorption of energy
Response in a flucating field

10. Solution fo linear equations: eigenfunction expansions .. 185
Eigenfunctions and eigenvalues
Generalised eigenfunctions and eigenvalues
Solution of two-term difference-differential equations
Exactly solvable recursion relations

11. Two- and three-level Hamiltonian systems ............... 199
Exactly solvable two-level systems
$N$ two-level systems
Exactly solvable three-level systems
Effective two-level approximations

12. Dissipative atomic systems ............................. 215
Two-level atom in quasimonochromatic field
$N$ two-level atoms in quasimonochromatic field
Two-level atoms in a fluctuating field
Driven three-level atom

13. Dissipative field-dynamics ............................. 239
Down-conversion in a damped cavity
Field interacting with two-photon reservoir
Reservoir in $\lambda$ configuration

14. Dissipative cavity QED ................................. 251
Two-level atoms in a single-mode cavity
Strong atom-field coupling
Response to external field
Micromaser

Appendices ................................................. 267

References ................................................. 277

Index ...................................................... 283