Download or read book Formulation and Numerical Solution of Quantum Control Problems written by Alfio Borzi and published by SIAM. This book was released on 2017-07-06 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Schr?dinger 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.

Download or read book Numerical Solution of the Schr dinger Equation written by Theodore E. Simos and published by World Scientific Publishing Company. This book was released on 2009 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title is devoted to the numerical solution of general problems with periodic and oscillating solutions.

Download or read book A New Method for the Numerical Solution of the Schr dinger Equation written by Raymond Clifford Grimm and published by . This book was released on 1970 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Discrete Nonlinear Schr dinger Equation written by Panayotis G. Kevrekidis and published by Springer Science & Business Media. This book was released on 2009-07-07 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical settings that it describes.

Download or read book Conceptual Foundations Of Quantum Mechanics written by Bernard D'espagnat and published by CRC Press. This book was released on 2018-03-05 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conceptual Foundations of Quantum Mechanics provides a detailed view of the conceptual foundations and problems of quantum physics, and a clear and comprehensive account of the fundamental physical implications of the quantum formalism. This book deals with nonseparability, hidden variable theories, measurement theories and several related problems. Mathematical arguments are presented with an emphasis on simple but adequately representative cases. The conclusion incorporates a description of a set of relationships and concepts that could compose a legitimate view of the world.

Download or read book Solving the Schrodinger Equation written by Paul L. A. Popelier and published by World Scientific. This book was released on 2011 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Schrodinger equation is the master equation of quantum chemistry. The founders of quantum mechanics realised how this equation underpins essentially the whole of chemistry. However, they recognised that its exact application was much too complicated to be solvable at the time. More than two generations of researchers were left to work out how to achieve this ambitious goal for molecular systems of ever-increasing size. This book focuses on non-mainstream methods to solve the molecular electronic Schrodinger equation. Each method is based on a set of core ideas and this volume aims to explain these ideas clearly so that they become more accessible. By bringing together these non-standard methods, the book intends to inspire graduate students, postdoctoral researchers and academics to think of novel approaches. Is there a method out there that we have not thought of yet? Can we design a new method that combines the best of all worlds?

Download or read book Numerical Solution for Schrodinger s Equation written by James E. Miller and published by . This book was released on 1964 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometric Numerical Integration and Schr dinger Equations written by Erwan Faou and published by European Mathematical Society. This book was released on 2012 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of geometric numerical integration is the simulation of evolution equations possessing geometric properties over long periods of time. Of particular importance are Hamiltonian partial differential equations typically arising in application fields such as quantum mechanics or wave propagation phenomena. They exhibit many important dynamical features such as energy preservation and conservation of adiabatic invariants over long periods of time. In this setting, a natural question is how and to which extent the reproduction of such long-time qualitative behavior can be ensured by numerical schemes. Starting from numerical examples, these notes provide a detailed analysis of the Schrodinger equation in a simple setting (periodic boundary conditions, polynomial nonlinearities) approximated by symplectic splitting methods. Analysis of stability and instability phenomena induced by space and time discretization are given, and rigorous mathematical explanations are provided for them. The book grew out of a graduate-level course and is of interest to researchers and students seeking an introduction to the subject matter.

Download or read book A Method Of Lines In The Numerical Solution Of Schr dinger Equation written by Lawal Sa'adu and published by LAP Lambert Academic Publishing. This book was released on 2012 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Method of Lines (MOL) has been one of the simplest but effective technique for solving partial differential equations (PDEs) in which all but one dimension is discretized. This work describes numerical solution of 1-dimensional Schrodinger equation using the method of lines approach (MOL) where spatial dimensions were discretized using some finite difference approximation leaving the time dimension to be the only independent variable in the resulting system of initial value problems. The effect of changing the discretization size on the accuracy of the solution procedure versus changing the step size in the integration of the resulting differential equation was also studied with the incorporation of Simpson's rule function in MATLAB.

Download or read book A NUMERICAL SOLUTION OF SCHRODINGER S EQUATION IN THE CONTINUUM written by United States. National Bureau of Standards and published by . This book was released on 1953 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Solution of the Schrodinger Equation for Different Types of Potentials written by Soon C. Park and published by . This book was released on 1987 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A High Order Method for the Numerical Solution of the Schr dinger Equation written by M. Rizea and published by . This book was released on 1980 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Simple Accurate Method for the Numerical Solution of the Schr dinger Equation written by Theodore E. Simos and published by . This book was released on 1997 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Nonlinear Schr dinger Equation written by Gadi Fibich and published by Springer. This book was released on 2015-03-06 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results. The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. Gadi Fibich is a Professor of Applied Mathematics at Tel Aviv University. “This book provides a clear presentation of the nonlinear Schrodinger equation and its applications from various perspectives (rigorous analysis, informal analysis, and physics). It will be extremely useful for students and researchers who enter this field.” Frank Merle, Université de Cergy-Pontoise and Institut des Hautes Études Scientifiques, France

Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

Download or read book Invariant Measures for Stochastic Nonlinear Schr dinger Equations written by Jialin Hong and published by Springer Nature. This book was released on 2019-08-22 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations. This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.

Download or read book Numerical Solution of the Schr dinger Equation on Unbounded Domains written by Maike Schulte and published by . This book was released on 2007 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: