# Mathematical Methods of Quantum Optics

Part of the Springer Series in Optical Sciences book series (SSOS, volume 79)

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Part of the Springer Series in Optical Sciences book series (SSOS, volume 79)

This book provides an accessible introduction to the mathematical methods of quantum optics. Starting from first principles, it reveals how a given system of atoms and a field is mathematically modelled. The method of eigenfunction expansion and the Lie algebraic method for solving equations are outlined. Analytically exactly solvable classes of equations are identified. The text also discusses consequences of Lie algebraic properties of Hamiltonians, such as the classification of their states as coherent, classical or non-classical based on the generalized uncertainty relation and the concept of quasiprobability distributions. A unified approach is developed for determining the dynamics of a two-level and a three-level atom interacting with combinations of quantized fields under certain conditions. Simple methods for solving a variety of linear and nonlinear dissipative master equations are given. The book will be valuable to newcomers to the field and to experimentalists in quantum optics.

Absorption Finite Lie algebra average equation function optics quantum mechanics quantum optics recursion variable

- DOI https://doi.org/10.1007/978-3-540-44953-9
- Copyright Information Springer-Verlag Berlin Heidelberg 2001
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Springer Book Archive
- Print ISBN 978-3-642-08732-5
- Online ISBN 978-3-540-44953-9
- Series Print ISSN 0342-4111
- Series Online ISSN 1556-1534
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