The Matrix Perturbation Method In Quantum Mechanics

Author : Francisco Soto-Eguibar
Publisher : Springer Nature
ISBN 13 : 3031485467
Total Pages : 201 pages
Book Rating : 4.66/5 ( download)

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Download or read book The Matrix Perturbation Method in Quantum Mechanics written by Francisco Soto-Eguibar and published by Springer Nature. This book was released on 2024-02-20 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an alternative approach to time-independent perturbation theory in non-relativistic quantum mechanics. It allows easy application to any initial condition because it is based on an approximation to the evolution operator and may also be used on unitary evolution operators for the unperturbed Hamiltonian in the case where the eigenvalues cannot be found. This flexibility sets it apart from conventional perturbation theory. The matrix perturbation method also gives new theoretical insights; for example, it provides corrections to the energy and wave function in one operation. Another notable highlight is the facility to readily derive a general expression for the normalization constant at m-th order, a significant difference between the approach within and those already in the literature. Another unique aspect of the matrix perturbation method is that it can be extended directly to the Lindblad master equation. The first and second-order corrections are obtained for this equation and the method is generalized for higher orders. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained. Throughout the book, several benchmark examples and practical applications underscore the potential, accuracy and good performance of this novel approach. Moreover, the method's applicability extends to some specific time-dependent Hamiltonians. This book represents a valuable addition to the literature on perturbation theory in quantum mechanics and is accessible to students and researchers alike.

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
ISBN 13 : 1461418054
Total Pages : 1885 pages
Book Rating : 4.54/5 ( download)

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Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Author : M. Konstantinov
Publisher : Gulf Professional Publishing
ISBN 13 : 0080538673
Total Pages : 443 pages
Book Rating : 4.79/5 ( download)

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Download or read book Perturbation Theory for Matrix Equations written by M. Konstantinov and published by Gulf Professional Publishing. This book was released on 2003-05-20 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the perturbation analysis of matrix equations. The importance of perturbation analysis is that it gives a way to estimate the influence of measurement and/or parametric errors in mathematical models together with the rounding errors done in the computational process. The perturbation bounds may further be incorporated in accuracy estimates for the solution computed in finite arithmetic. This is necessary for the development of reliable computational methods, algorithms and software from the viewpoint of modern numerical analysis. In this book a general perturbation theory for matrix algebraic equations is presented. Local and non-local perturbation bounds are derived for general types of matrix equations as well as for the most important equations arising in linear algebra and control theory. A large number of examples, tables and figures is included in order to illustrate the perturbation techniques and bounds. Key features: • The first book in this field • Can be used by a variety of specialists • Material is self-contained • Results can be used in the development of reliable computational algorithms • A large number of examples and graphical illustrations are given • Written by prominent specialists in the field

Author : Jagdish Mehra
Publisher : Springer Science & Business Media
ISBN 13 : 9780387951775
Total Pages : 346 pages
Book Rating : 4.76/5 ( download)

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Download or read book The Historical Development of Quantum Theory written by Jagdish Mehra and published by Springer Science & Business Media. This book was released on 2000-12-28 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Theory, together with the principles of special and general relativity, constitute a scientific revolution that has profoundly influenced the way in which we think about the universe and the fundamental forces that govern it. The Historical Development of Quantum Theory is a definitive historical study of that scientific work and the human struggles that accompanied it from the beginning. Drawing upon such materials as the resources of the Archives for the History of Quantum Physics, the Niels Bohr Archives, and the archives and scientific correspondence of the principal quantum physicists, as well as Jagdish Mehra's personal discussions over many years with most of the architects of quantum theory, the authors have written a rigorous scientific history of quantum theory in a deeply human context. This multivolume work presents a rich account of an intellectual triumph: a unique analysis of the creative scientific process. The Historical Development of Quantum Theory is science, history, and biography, all wrapped in the story of a great human enterprise. Its lessons will be an aid to those working in the sciences and humanities alike.

Author : G. W. Stewart
Publisher : Academic Press
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.54/5 ( download)

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Download or read book Matrix Perturbation Theory written by G. W. Stewart and published by Academic Press. This book was released on 1990-06-28 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive survey of matrix perturbation theory, a topic of interest to numerical analysts, statisticians, physical scientists, and engineers. In particular, the authors cover perturbation theory of linear systems and least square problems, the eignevalue problem, and the generalized eignevalue problem as wellas a complete treatment of vector and matrix norms, including the theory of unitary invariant norms.

Author : Edward Michael Corson
Publisher :
ISBN 13 :
Total Pages : 328 pages
Book Rating : 4.79/5 ( download)

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Download or read book Perturbation Methods in the Quantum Mechanics of N-electron Systems written by Edward Michael Corson and published by . This book was released on 1951 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : K.T. Hecht
Publisher : Springer Science & Business Media
ISBN 13 : 9780387989198
Total Pages : 794 pages
Book Rating : 4.96/5 ( download)

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Download or read book Quantum Mechanics written by K.T. Hecht and published by Springer Science & Business Media. This book was released on 2000-05-19 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for a first-year graduate course in quantum mechanics, this text provides a thorough introduction to the subject. The first half of the book emphasizes bound-state problems. It begins with the familiar approach via differential equations and coordinate representations. A discussion of the factorization method and ladder operators for solving the eigenvalue problem leads naturally to the modern algebraic approach. Part II treats time-independent perturbation theory. The role of symmetry breaking in removing degeneracies is emphasized, but cases in which the first-order perturbation does not lead to the proper symmetry-adapted basis are also treated. Part III provides a detailed discussion of rotational symmetry and angular momentum, including the Wigner-Eckart theorem, and the matrix elements of the general rotation operator and of vector-coupled tensor operators in terms of angular momentum recoupling coefficients. It includes a chapter on the SO (2,1) algebra of a stretched Coulomb basis that avoids the infinite sum and continuum contributions of conventional perturbation treatments. Part IV provides an introduction to systems of identical particles. The second half deals chiefly with continuum problems : scattering theory, including rearrangement collisions ; a discussion of density matrices and statistical distributions of states ; time-dependent perturbation theory ; and atom-photon interactions, including the full multipole expansion of the quantized electromagnetic field. The book concludes with the Dirac theory of spin 1/2 particles and an introduction to many-body theory using annihilation-creation operator formalism. The text is self-contained and can be used by students without a previous course in quantum mechanics. Numerous problems are an integral part of the text, guiding and testing the reader's understanding.

Author : Ta-you Wu
Publisher : World Scientific Publishing Company
ISBN 13 : 981310399X
Total Pages : 435 pages
Book Rating : 4.93/5 ( download)

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Download or read book Quantum Mechanics written by Ta-you Wu and published by World Scientific Publishing Company. This book was released on 1986-05-01 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a distillation of Prof T Y Wu's fifty years of experience teaching quantum theory to many generations of physicists. Starting with chapters on classical physics and the old quantum theory, Prof Wu quickly develops Heisenberg's matrix mechanics and the Schroedinger equation. After a detailed treatment of the general formulation of quantum theory, standard discussions on Perturbation Theory and the Hydrogen Atom follow. A fairly exhaustive treatment of the Zeeman effect is to be found in these chapter. Many electron atoms are treated expertly. The former is treated with great depth; the latter is a good introduction to the subject.

Author : Tosio Kato
Publisher : Springer Science & Business Media
ISBN 13 : 3662126788
Total Pages : 610 pages
Book Rating : 4.83/5 ( download)

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Download or read book Perturbation theory for linear operators written by Tosio Kato and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Richard Ernest Bellman
Publisher : Courier Corporation
ISBN 13 : 9780486432588
Total Pages : 146 pages
Book Rating : 4.80/5 ( download)

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Download or read book Perturbation Techniques in Mathematics, Engineering and Physics written by Richard Ernest Bellman and published by Courier Corporation. This book was released on 2003-01-01 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate students receive a stimulating introduction to analytical approximation techniques for solving differential equations in this text, which introduces scientifically significant problems and indicates useful solutions. 1966 edition.