General Quantum Numerical Analysis
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General Quantum Numerical Analysis
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Author : Svetlin G. Georgiev
language : en
Publisher: CRC Press
Release Date : 2024-05-03
General Quantum Numerical Analysis written by Svetlin G. Georgiev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-03 with Mathematics categories.
This book is focused on the qualitative theory of general quantum calculus, the modern name for the investigation of calculus without limits. It centers on designing, analysing and applying computational techniques for general quantum differential equations. The quantum calculus or q-calculus began with F.H. Jackson in the early twentieth century, but this kind of calculus had already been worked out by Euler and Jacobi. Recently, it has aroused interest due to high demand of mathematics that models quantum computing and the connection between mathematics and physics. Quantum calculus has many applications in different mathematical areas such as number theory, combinatorics, orthogonal polynomials, basic hyper-geometric functions and other sciences such as quantum theory, mechanics and the theory of relativity. The authors summarize the most recent contributions in this area. General Quantum Numerical Analysis is intended for senior undergraduate students and beginning graduate students of engineering and science courses. The twelve chapters in this book are pedagogically organized, each concluding with a section of practical problems.
Tensor Numerical Methods In Quantum Chemistry
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Author : Venera Khoromskaia
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-06-11
Tensor Numerical Methods In Quantum Chemistry written by Venera Khoromskaia and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-11 with Mathematics categories.
The conventional numerical methods when applied to multidimensional problems suffer from the so-called "curse of dimensionality", that cannot be eliminated by using parallel architectures and high performance computing. The novel tensor numerical methods are based on a "smart" rank-structured tensor representation of the multivariate functions and operators discretized on Cartesian grids thus reducing solution of the multidimensional integral-differential equations to 1D calculations. We explain basic tensor formats and algorithms and show how the orthogonal Tucker tensor decomposition originating from chemometrics made a revolution in numerical analysis, relying on rigorous results from approximation theory. Benefits of tensor approach are demonstrated in ab-initio electronic structure calculations. Computation of the 3D convolution integrals for functions with multiple singularities is replaced by a sequence of 1D operations, thus enabling accurate MATLAB calculations on a laptop using 3D uniform tensor grids of the size up to 1015. Fast tensor-based Hartree-Fock solver, incorporating the grid-based low-rank factorization of the two-electron integrals, serves as a prerequisite for economical calculation of the excitation energies of molecules. Tensor approach suggests efficient grid-based numerical treatment of the long-range electrostatic potentials on large 3D finite lattices with defects.The novel range-separated tensor format applies to interaction potentials of multi-particle systems of general type opening the new prospects for tensor methods in scientific computing. This research monograph presenting the modern tensor techniques applied to problems in quantum chemistry may be interesting for a wide audience of students and scientists working in computational chemistry, material science and scientific computing.
Quantum Geometry
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Author : Margaret Prugovecki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Quantum Geometry written by Margaret Prugovecki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Science categories.
This monograph presents a review and analysis of the main mathematical, physical and epistomological difficulties encountered at the foundational level by all the conventional formulations of relativistic quantum theories, ranging from relativistic quantum mechanics and quantum field theory in Minkowski space, to the various canonical and covariant approaches to quantum gravity. It is, however, primarily devoted to the systematic presentation of a quantum framework meant to deal effectively with these difficulties by reconsidering the foundations of these subjects, analyzing their epistemic nature, and then developing mathematical tools which are specifically designed for the elimination of all the basic inconsistencies. A carefully documented historical survey is included, and additional extensive notes containing quotations from original sources are incorporated at the end of each chapter, so that the reader will be brought up-to-date with the very latest developments in quantum field theory in curved spacetime, quantum gravity and quantum cosmology. The survey further provides a backdrop against which the new foundational and mathematical ideas of the present approach to these subjects can be brought out in sharper relief.
Quantum Computation And Information
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Author : Hiroshi Imai
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-12
Quantum Computation And Information written by Hiroshi Imai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-12 with Science categories.
This book reviews selected topics charterized by great progress and covers the field from theoretical areas to experimental ones. It contains fundamental areas, quantum query complexity, quantum statistical inference, quantum cloning, quantum entanglement, additivity. It treats three types of quantum security system, quantum public key cryptography, quantum key distribution, and quantum steganography. A photonic system is highlighted for the realization of quantum information processing.
Quantum Mechanics
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Author : Louis Marchildon
language : en
Publisher: Springer
Release Date : 2010-12-05
Quantum Mechanics written by Louis Marchildon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-05 with Science categories.
This fresh and original text on quantum mechanics focuses on: the development of numerical methods for obtaining specific results; the presentation of group theory and the systematic use of operators; the introduction of the functional integral and its applications in approximation; the discussion of distant correlations and experimental measurements. Numerous exercises with hints and solutions, examples and applications, and a guide to key references help the student to work with the text.
Computational Methods For Physics
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Author : Joel Franklin
language : en
Publisher: Cambridge University Press
Release Date : 2013-05-23
Computational Methods For Physics written by Joel Franklin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-23 with Science categories.
Presenting mathematical techniques for physical problems, this textbook is invaluable for undergraduate students in physics.
Computational Physics
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Author : Philipp Scherer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-17
Computational Physics written by Philipp Scherer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-17 with Science categories.
This textbook presents basic and advanced computational physics in a very didactic style. It contains very-well-presented and simple mathematical descriptions of many of the most important algorithms used in computational physics. The first part of the book discusses the basic numerical methods. The second part concentrates on simulation of classical and quantum systems. Several classes of integration methods are discussed including not only the standard Euler and Runge Kutta method but also multi-step methods and the class of Verlet methods, which is introduced by studying the motion in Liouville space. A general chapter on the numerical treatment of differential equations provides methods of finite differences, finite volumes, finite elements and boundary elements together with spectral methods and weighted residual based methods. The book gives simple but non trivial examples from a broad range of physical topics trying to give the reader insight into not only the numerical treatment but also simulated problems. Different methods are compared with regard to their stability and efficiency. The exercises in the book are realised as computer experiments.
Advanced Calculus And Its Applications In Variational Quantum Mechanics And Relativity Theory
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Author : Fabio Silva Botelho
language : en
Publisher: CRC Press
Release Date : 2021-07-12
Advanced Calculus And Its Applications In Variational Quantum Mechanics And Relativity Theory written by Fabio Silva Botelho and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-12 with Mathematics categories.
Presents a rigorous study on manifolds in Rn. Develops in details important standard topics on advanced calculus, such as the differential forms in surfaces in Rn. Presents a proposal to connect classical and quantum mechanics. Presents variational formulations for relativistic mechanics through semi-Riemannian geometry and differential geometry. Develops a rigorous study on causal structures in space-time manifolds.
The Birth Of Numerical Analysis
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Author : Adhemar Bultheel
language : en
Publisher: World Scientific
Release Date : 2010
The Birth Of Numerical Analysis written by Adhemar Bultheel and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
The 1947 paper by John von Neumann & Herman Goldstine, 'Numerical Inverting of Matrices of High Order', is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous. This book collects contributions by researchers who have lived through this evolution.
Asymptotic Methods In Quantum Mechanics
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Author : S.H. Patil
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Methods In Quantum Mechanics written by S.H. Patil and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Quantum mechanics and the Schrodinger equation are the basis for the de scription of the properties of atoms, molecules, and nuclei. The development of reliable, meaningful solutions for the energy eigenfunctions of these many is a formidable problem. The usual approach for obtaining particle systems the eigenfunctions is based on their variational extremum property of the expectation values of the energy. However the complexity of these variational solutions does not allow a transparent, compact description of the physical structure. There are some properties of the wave functions in some specific, spatial domains, which depend on the general structure of the Schrodinger equation and the electromagnetic potential. These properties provide very useful guidelines in developing simple and accurate solutions for the wave functions of these systems, and provide significant insight into their physical structure. This point, though of considerable importance, has not received adequate attention. Here we present a description of the local properties of the wave functions of a collection of particles, in particular the asymptotic properties when one of the particles is far away from the others. The asymptotic behaviour of this wave function depends primarily on the separation energy of the outmost particle. The universal significance of the asymptotic behaviour of the wave functions should be appreciated at both research and pedagogic levels. This is the main aim of our presentation here.