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Full Description
This book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the Schrödinger picture, and the optimization theory, which focuses on functional spaces, is based on the Lagrange formalism. The computational techniques represent recent developments that have resulted from combining modern numerical techniques for quantum evolutionary equations with sophisticated optimization schemes. Both finite and infinite-dimensional models are discussed, including the three-level Lambda system arising in quantum optics, multispin systems in NMR, a charged particle in a well potential, Bose-Einstein condensates, multiparticle spin systems, and multiparticle models in the time-dependent density functional framework.
This self-contained book covers the formulation, analysis, and numerical solution of quantum control problems and bridges scientific computing, optimal control and exact controllability, optimization with differential models, and the sciences and engineering that require quantum control methods.
Contents
Preface
Chapter 1: Introduction
Chapter 2: Quantum mechanics and the Schrödinger equation
Chapter 3: Optimal control theory for quantum systems
Chapter 4: Controllability of quantum systems
Chapter 5: Discretization schemes
Chapter 6: Numerical optimization methods
Chapter 7: Application to quantum control problems
Appendix
Bibliography
Index
