## Methods in Theoretical Quantum OpticsMethods in theoretical quantum optics is aimed at those readers who already have some knowledge of mathematical methods and have also been introduced to the basic ideas of quantum optics. This book is ideal for students who have already explored the basics of the quantum theory of light and are seeking to acquire the mathematical skills used in real problems. This book is not primarily about the physics of quantum optics, but rather presents the mathematical methods widely used by workers in this field. There is no comparable book which covers either the range or the depth of mathematical techniques. |

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### Contents

Foundations | 1 |

Operators and states | 34 |

Quantum statistics of fields | 87 |

Dissipative processes | 130 |

Dressed states | 182 |

Kronecker delta and the permutation symbol | 222 |

Special functions | 228 |

Quadrature eigenstates | 234 |

The pole approximation | 240 |

Laplace transforms and the final value theorem | 250 |

The method of characteristics for partial differential | 258 |

FokkerPlanck equations | 266 |

Cubic equations | 276 |

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### Common terms and phrases

action amplitude annihilation operators Appendix applied approximation associated atom basis becomes calculate Chapter characteristic function coherent commutator Comparing complete condition consider constant contains continuum correlation corresponding coupling creation decay defined density matrix depends derivative described differential equation discrete discussed distribution dressed effect eigenstates eigenvalue energy environment equal evaluated evolution example expectation value exponential expressed fact factor field final follows frequency given gives Hamiltonian Hence Hermitian identity important independent initial integral interaction leads limit mean method mode moments normal ordered number operator obtain optics peak phase photon number picture pole positive possible probability properties quadrature quantum quasi-probability relation replaced resonance respectively result satisfy simple single single-mode sinh solution solve spectrum squeezed stochastic differential equations Substituting taking theorem transform transitions vacuum variance write written zero