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