Mathematical Methods Of Quantum Optics - Puri R R - Berlin, Springer, 2001, Pp Xiii 285.pdf

MATHEMATICAL METHODS OF QUANTUM OPTICS
Berlin: Springer, 2001, pp. XIII+285
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 two-level and a three- level atom binations of
quantized fields under certain conditions. Simple methods for solving a variety of linear
and nonlinear dissipative master equations are given.
Contents
1. Basic Quantum Mechanics 1
Postulates of Quantum Mechanics 1
Postulate 1 1
Postulate 2 11
Postulate 3 11
Postulate 4 11
Postulate 5 13
Geometric Phase 16
Geometric Phase of a Harmonic Oscillator 18
Geometric Phase of a Two-Level System 18
Geometric Phase in Adiabatic Evolution 18
Time-Dependent Approximation Method 19
Quantum Mechanics of posite System 20
Quantum Mechanics of a Subsystem and Density Operator 21
Systems of One and Two Spin-l/2s 23
Wave-Particle Duality 26
Measurement Postulate and Paradoxes of Quantum Theory 29
The Measurement Problem 30
Schrödinger's Cat Paradox 31
EPR Paradox 32
Local Hidden Variables Theory 34
2. Algebra of the Exponential Operator 37
Parametric Differentiation of the Exponential 37
Exponential of a Finite-Dimensional Operator 38
Lie Algebraic Similarity Trans