The Matrix Perturbation Method In Quantum Mechanics

Author : Francisco Soto-Eguibar,Braulio Misael Villegas-Martínez,Héctor Manuel Moya-Cessa
Publisher : Springer Nature
Page : 201 pages
File Size : 46,9 Mb
Release : 2024-02-20
Category : Science
ISBN : 9783031485466

Get Book

The Matrix Perturbation Method in Quantum Mechanics by Francisco Soto-Eguibar,Braulio Misael Villegas-Martínez,Héctor Manuel Moya-Cessa Pdf

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 : Bryce S. DeWitt
Publisher : Unknown
Page : 294 pages
File Size : 45,8 Mb
Release : 1955
Category : Electronic
ISBN : UOM:39015077590290

Get Book

The Operator Formalism in Quantum Perturbation Theory by Bryce S. DeWitt Pdf

Author : Francisco M. Fernandez
Publisher : CRC Press
Page : 289 pages
File Size : 55,5 Mb
Release : 2000-09-19
Category : Science
ISBN : 9781420039641

Get Book

Introduction to Perturbation Theory in Quantum Mechanics by Francisco M. Fernandez Pdf

Perturbation theory is a powerful tool for solving a wide variety of problems in applied mathematics, a tool particularly useful in quantum mechanics and chemistry. Although most books on these subjects include a section offering an overview of perturbation theory, few, if any, take a practical approach that addresses its actual implementation

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
Page : 1885 pages
File Size : 50,8 Mb
Release : 2011-10-05
Category : Mathematics
ISBN : 9781461418054

Get Book

Mathematics of Complexity and Dynamical Systems by Robert A. Meyers Pdf

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 : K.T. Hecht
Publisher : Springer Science & Business Media
Page : 794 pages
File Size : 46,6 Mb
Release : 2000-05-19
Category : Science
ISBN : 0387989196

Get Book

Quantum Mechanics by K.T. Hecht Pdf

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 : Jagdish Mehra,Helmut Rechenberg
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 41,5 Mb
Release : 2000-12-28
Category : Science
ISBN : 0387951776

Get Book

The Historical Development of Quantum Theory by Jagdish Mehra,Helmut Rechenberg Pdf

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 : Gustavo A. Arteca,Francisco M. Fernandez,Eduardo A. Castro
Publisher : Springer Science & Business Media
Page : 655 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642934698

Get Book

Large Order Perturbation Theory and Summation Methods in Quantum Mechanics by Gustavo A. Arteca,Francisco M. Fernandez,Eduardo A. Castro Pdf

The book provides a general, broad approach to aspects of perturbation theory. The aim has been to cover all topics of interest, from construction, analysis, and summation of perturbation series to applications. Emphasis is placed on simple methods, as well as clear, intuitive ideas stemming from the physics of systems of interest.

Author : Ta-you Wu
Publisher : World Scientific Publishing Company
Page : 435 pages
File Size : 51,6 Mb
Release : 1986-05-01
Category : Electronic
ISBN : 9789813103993

Get Book

Quantum Mechanics by Ta-you Wu Pdf

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 : F. Constantinescu,E. Magyari
Publisher : Elsevier
Page : 429 pages
File Size : 52,7 Mb
Release : 2013-10-22
Category : Science
ISBN : 9781483292946

Get Book

Problems in Quantum Mechanics by F. Constantinescu,E. Magyari Pdf

International Series in Natural Philosophy, Volume 30: Problems in Quantum Mechanics focuses on the processes, principles, reactions, and methodologies involved in quantum mechanics. The publication first elaborates on the mathematical formalism of quantum mechanics, simple quantum systems, and mean values and uncertainty relations. Discussions focus on mean values of dynamical variables, uncertainty relations, eigenfunctions and the energy spectrum, motion in a central field, matrix representation of vectors and operators, Hubert spaces, and operators in Hilbert space. The text then takes a look at mean values and uncertainty relations, semi-classical approximation, and pictures and representations. The book takes a look at orbital angular momentum and spin, systems of identical particles, and perturbation theory. Topics include variational method, stationary state perturbation theory, isotopic spin, second quantization, properties of angular momentum operators, and angular momentum and rotations of coordinate axes. The manuscript also ponders on functions used in quantum mechanics, relativistic quantum mechanics, and radiation theory. The publication is a dependable reference for researchers interested in quantum mechanics.

Author : Kailash Kumar
Publisher : Courier Dover Publications
Page : 256 pages
File Size : 40,6 Mb
Release : 2017-09-20
Category : Science
ISBN : 9780486825809

Get Book

Perturbation Theory and the Nuclear Many Body Problem by Kailash Kumar Pdf

Introductory treatment provides overview of basics and diagrammatic methods. Topics include rearrangement methods and techniques of solving the t-matrix and other equations that arise in the nuclear many body problem. 1962 edition.

Author : Calvin Hayden Wilcox
Publisher : Unknown
Page : 448 pages
File Size : 43,9 Mb
Release : 1966
Category : Perturbation (Quantum dynamics)
ISBN : STANFORD:36105032052479

Get Book

Perturbation Theory and Its Applications in Quantum Mechanics by Calvin Hayden Wilcox Pdf

Author : Maxim Olchanyi (Olshanii)
Publisher : World Scientific
Page : 223 pages
File Size : 46,6 Mb
Release : 2024-01-10
Category : Science
ISBN : 9789811286391

Get Book

Back-of-the-envelope Quantum Mechanics: With Extensions To Many-body Systems, Integrable Pdes, And Rare And Exotic Methods (Second Edition) by Maxim Olchanyi (Olshanii) Pdf

Dimensional and order-of-magnitude estimates are practiced by almost everybody but taught almost nowhere. When physics students engage in their first theoretical research project, they soon learn that exactly solvable problems belong only to textbooks, that numerical models are long and resource consuming, and that 'something else' is needed to quickly gain insight into the system they are going to study. Qualitative methods are this 'something else', but typically, students have never heard of them before.The aim of this book is to teach the craft of qualitative analysis using a set of problems, some with solutions and some without, in advanced undergraduate and beginning graduate Quantum Mechanics. Examples include a dimensional analysis solution for the spectrum of a quartic oscillator, simple WKB formulas for the matrix elements of a coordinate in a gravitational well, and a three-line-long estimate for the ionization energy of atoms uniformly valid across the whole periodic table. The pièce de résistance in the collection is a series of dimensional analysis questions in Integrable Nonlinear Partial Differential Equations with no dimensions existing a priori. Solved problems include the relationship between the size and the speed of solitons of the Korteweg-de Vries equation and an expression for the oscillation period of a Nonlinear Schrödinger breather as a function of its width.A new theme that appears in the second edition are the rare and exotic methods in elementary quantum mechanics. The new chapter covers quantum-mechanical supersymmetry, power index method, scale invariance, self-similarity, and circle inversion.

Author : Migdal
Publisher : CRC Press
Page : 464 pages
File Size : 49,8 Mb
Release : 2018-03-05
Category : Science
ISBN : 9780429966491

Get Book

Qualitative Methods In Quantum Theory by Migdal Pdf

This unique book, written by a leading Soviet theorist, is not a textbook of quantum mechanics but rather a compendium of the "tricks of the trade"-the methods that all practicing theoretical physicists use but few have set down in writing.

Author : Barry G. Adams
Publisher : Springer Science & Business Media
Page : 457 pages
File Size : 46,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642579332

Get Book

Algebraic Approach to Simple Quantum Systems by Barry G. Adams Pdf

This book provides an introduction to the use of algebraic methods and sym bolic computation for simple quantum systems with applications to large order perturbation theory. It is the first book to integrate Lie algebras, algebraic perturbation theory and symbolic computation in a form suitable for students and researchers in theoretical and computational chemistry and is conveniently divided into two parts. The first part, Chapters 1 to 6, provides a pedagogical introduction to the important Lie algebras so(3), so(2,1), so(4) and so(4,2) needed for the study of simple quantum systems such as the D-dimensional hydrogen atom and harmonic oscillator. This material is suitable for advanced undergraduate and beginning graduate students. Of particular importance is the use of so(2,1) in Chapter 4 as a spectrum generating algebra for several important systems such as the non-relativistic hydrogen atom and the relativistic Klein-Gordon and Dirac equations. This approach provides an interesting and important alternative to the usual textbook approach using series solutions of differential equations.

Author : Debdeep Jena
Publisher : Oxford University Press
Page : 897 pages
File Size : 45,6 Mb
Release : 2022-06-25
Category : Science
ISBN : 9780198856849

Get Book

Quantum Physics of Semiconductor Materials and Devices by Debdeep Jena Pdf

"Quantum Phenomena do not occur in a Hilbert space. They occur in a laboratory". - Asher Peres Semiconductor physics is a laboratory to learn and discover the concepts of quantum mechanics and thermodynamics, condensed matter physics, and materials science, and the payoffs are almost immediate in the form of useful semiconductor devices. Debdeep Jena has had the opportunity to work on both sides of the fence - on the fundamental materials science and quantum physics of semiconductors, and in their applications in semiconductor electronic and photonic devices. In Quantum Physics of Semiconductors and Nanostructures, Jena uses this experience to make each topic as tangible and accessible as possible to students at all levels. Consider the simplest physical processes that occur in semiconductors: electron or hole transport in bands and over barriers, collision of electrons with the atoms in the crystal, or when electrons and holes annihilate each other to produce a photon. The correct explanation of these processes require a quantum mechanical treatment. Any shortcuts lead to misconceptions that can take years to dispel, and sometimes become roadblocks towards a deeper understanding and appreciation of the richness of the subject. A typical introductory course on semiconductor physics would then require prerequisites of quantum mechanics, statistical physics and thermodynamics, materials science, and electromagnetism. Rarely would a student have all this background when (s)he takes a course of this nature in most universities. Jena's work fills in these gaps and gives students the background and deeper understanding of the quantum physics of semiconductors and nanostructures.