Download or read book Schrodinger Operators the Quantum Mechanical Many Body Problem written by Erik Balslev and published by . This book was released on 2014-10-02 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Schr dinger Operators written by Erik Balslev and published by Springer. This book was released on 1992 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Many Body Schr dinger Equation written by Hiroshi Isozaki and published by Springer Nature. This book was released on 2023-08-28 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral properties for Schrödinger operators are a major concern in quantum mechanics both in physics and in mathematics. For the few-particle systems, we now have sufficient knowledge for two-body systems, although much less is known about N-body systems. The asymptotic completeness of time-dependent wave operators was proved in the 1980s and was a landmark in the study of the N-body problem. However, many problems are left open for the stationary N-particle equation. Due to the recent rapid development of computer power, it is now possible to compute the three-body scattering problem numerically, in which the stationary formulation of scattering is used. This means that the stationary theory for N-body Schrödinger operators remains an important problem of quantum mechanics. It is stressed here that for the three-body problem, we have a satisfactory stationary theory. This book is devoted to the mathematical aspects of the N-body problem from both the time-dependent and stationary viewpoints. The main themes are:(1) The Mourre theory for the resolvent of self-adjoint operators(2) Two-body Schrödinger operators—Time-dependent approach and stationary approach(3) Time-dependent approach to N-body Schrödinger operators(4) Eigenfunction expansion theory for three-body Schrödinger operatorsCompared with existing books for the many-body problem, the salient feature of this book consists in the stationary scattering theory (4). The eigenfunction expansion theorem is the physical basis of Schrödinger operators. Recently, it proved to be the basis of inverse problems of quantum scattering. This book provides necessary background information to understand the physical and mathematical basis of Schrödinger operators and standard knowledge for future development.

Download or read book The Quantum Mechanics of Many Body Systems written by D. J. Thouless and published by Academic Press. This book was released on 2013-10-22 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Quantum Mechanics of Many-Body Systems provides an introduction to that field of theoretical physics known as ""many-body theory."" It is concerned with problems that are common to nuclear physics, atomic physics, the electron theory of metals, and to the theories of liquid helium three and four, and it describes the methods which have recently been developed to solve such problems. The aim has been to produce a unified account of the field, rather than to describe all the parallel methods that have been developed; as a result, a number of important papers are not mentioned. The main emphasis is on the theories of atomic nuclei, the electron gas, and liquid helium; there is no discussion of molecular theory or of solid helium. The reader is expected to be familiar with the principles of nonrelativistic quantum mechanics and of statistical mechanics, but a knowledge of field theory and a detailed knowledge of nuclear and solid state physics are not assumed.

Download or read book Schr dinger Operators written by Hans L. Cycon and published by Springer. This book was released on 2009-08-19 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete understanding of Schrödinger operators is a necessary prerequisite for unveiling the physics of nonrelativistic quanturn mechanics. Furthermore recent research shows that it also helps to deepen our insight into global differential geometry. This monograph written for both graduate students and researchers summarizes and synthesizes the theory of Schrödinger operators emphasizing the progress made in the last decade by Lieb, Enss, Witten and others. Besides general properties, the book covers, in particular, multiparticle quantum mechanics including bound states of Coulomb systems and scattering theory, quantum mechanics in constant electric and magnetic fields, Schrödinger operators with random and almost periodic potentials and, finally, Schrödinger operator methods in differential geometry to prove the Morse inequalities and the index theorem.

Download or read book Schr dinger Operators written by Hans L. Cycon and published by Springer Science & Business Media. This book was released on 1987 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Are you looking for a concise summary of the theory of Schrödinger operators? Here it is. Emphasizing the progress made in the last decade by Lieb, Enss, Witten and others, the three authors don’t just cover general properties, but also detail multiparticle quantum mechanics – including bound states of Coulomb systems and scattering theory. This corrected and extended reprint contains updated references as well as notes on the development in the field over the past twenty years.

Download or read book Introduction to Quantum Mechanics written by Horst R. Beyer and published by Springer Nature. This book was released on with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Defocusing Nonlinear Schr dinger Equation written by Panayotis G. Kevrekidis and published by SIAM. This book was released on 2015-08-04 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bose?Einstein condensation is a phase transition in which a fraction of particles of a boson gas condenses into the same quantum state known as the Bose?Einstein condensate (BEC). The aim of this book is to present a wide array of findings in the realm of BECs and on the nonlinear Schr?dinger-type models that arise therein. The Defocusing Nonlinear Schr?dinger Equation is a broad study of nonlinear excitations in self-defocusing nonlinear media. It summarizes state-of-the-art knowledge on the defocusing nonlinear Schr?dinger-type models in a single volume and contains a wealth of resources, including over 800 references to relevant articles and monographs and a meticulous index for ease of navigation.

Download or read book Quantum Statistical Mechanics written by Leo P. Kadanoff and published by CRC Press. This book was released on 2018-03-08 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a very early systematic treatment of the application of the field-theoretical methods developed after the Second World War to the quantum mechanical many-body problem at finite temperature. It describes various techniques that remain basic tools of modern condensed matter physicists.

Download or read book Topics in the Theory of Schr dinger Operators written by Huzihiro Araki and published by World Scientific. This book was released on 2004 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book presents reviews of some recent topics in the theory of Schr”dinger operators. It includes a short introduction to the subject, a survey of the theory of the Schr”dinger equation when the potential depends on the time periodically, an introduction to the so-called FBI transformation (also known as coherent state expansion) with application to the semi-classical limit of the S-matrix, an overview of inverse spectral and scattering problems, and a study of the ground state of the Pauli-Fierz model with the use of the functional integral. The material is accessible to graduate students and non-expert researchers.

Download or read book Schr dinger Operators written by Helge Holden and published by Springer. This book was released on 2013-11-20 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding quantum mechanics inevitably leads to an in-depth study of the Schrödinger operator. This set of review lectures informs researchers and advanced students of the most recent developments in the analysis of the Schrödinger operator occurring in solid-state physics, nuclear physics, etc. The topics covered are nonlinear and random potentials, magnetic fields, and many-body problems. Inverse spectral theory is also treated. The results are mathematically rigorous and many physical implications are discussed. The book is suitable for advanced courses in mathematical physics.

Download or read book Quantum Theory of Many Body Systems written by Alexandre Zagoskin and published by Springer. This book was released on 2016-09-10 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents a self-contained treatment of the physics of many-body systems from the point of view of condensed matter. The approach, quite traditionally, uses the mathematical formalism of quasiparticles and Green’s functions. In particular, it covers all the important diagram techniques for normal and superconducting systems, including the zero-temperature perturbation theory and the Matsubara, Keldysh and Nambu-Gor'kov formalism, as well as an introduction to Feynman path integrals. This new edition contains an introduction to the methods of theory of one-dimensional systems (bosonization and conformal field theory) and their applications to many-body problems. Intended for graduate students in physics and related fields, the aim is not to be exhaustive, but to present enough detail to enable the student to follow the current research literature, or to apply the techniques to new problems. Many of the examples are drawn from mesoscopic physics, which deals with systems small enough that quantum coherence is maintained throughout their volume and which therefore provides an ideal testing ground for many-body theories.

Download or read book Operator Methods in Quantum Mechanics written by Martin Schechter and published by Elsevier. This book was released on 2012-12-02 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operator Methods in Quantum Mechanics demonstrates the power of operator theory as a tool in the study of quantum mechanics. More specifically, it shows how to use algebraic, representation-independent methods to solve one- and three-dimensional problems, including certain relativistic problems. It explains the applications of commutation relations, shift operators, and the virial, hypervirial, and Hellman-Feyman theorems to the calculation of eigenvalues, matrix elements, and wave functions. Organized into 16 chapters, this book begins by presenting a few simple postulates describing quantum theory and looking at a single particle moving along a straight line. Then, it introduces mathematical techniques that answer questions about the particle. It also discusses the use of spectral theorem in answering various questions concerning observables, along with negative eigenvalues and methods of determining parts of the spectrum or estimating lower bounds. Moreover, it explains the time-independent or stationary-state scattering theory and states, long-range potentials, and completeness and strong completeness. Oscillating potentials, eigenfunction expansions, restricted particles, hard-core potentials, the invariance principle, and the use of trace class operators to treat scattering theory are also described in this book. This volume is a valuable resource for physicists, as well as students of intermediate quantum mechanics and postgraduate students who want to be acquainted with the algebraic method of solving quantum mechanical problems.

Download or read book Mathematical Methods in Quantum Mechanics written by Gerald Teschl and published by American Mathematical Soc.. This book was released on 2009 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).

Download or read book Back of the envelope Quantum Mechanics written by Maxim Olshanii and published by World Scientific. This book was released on 2014 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 pi ce de r(r)sistance 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 SchrAdinger breather as a function of its widt

Download or read book Schr dinger Operators Standard and Non standard written by Pavel Exner and published by . This book was released on 1989 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quantum Physics For Dummies written by Steven Holzner and published by John Wiley & Sons. This book was released on 2013-01-09 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Physics For Dummies, Revised Edition helps make quantum physics understandable and accessible. From what quantum physics can do for the world to understanding hydrogen atoms, readers will get complete coverage of the subject, along with numerous examples to help them tackle the tough equations. Compatible with classroom text books and courses, Quantum Physics For Dummies, Revised Edition lets students study at their own paces and helps them prepare for graduate or professional exams. Coverage includes: The Schrodinger Equation and its Applications The Foundations of Quantum Physics Vector Notation Spin Scattering Theory, Angular Momentum, and more Your plain-English guide to understanding and working with the micro world Quantum physics — also called quantum mechanics or quantum field theory — can be daunting for even the most dedicated student or enthusiast of science, math, or physics. This friendly, concise guide makes this challenging subject understandable and accessible, from atoms to particles to gases and beyond. Plus, it's packed with fully explained examples to help you tackle the tricky equations like a pro! Compatible with any classroom course — study at your own pace and prepare for graduate or professional exams Your journey begins here — understand what quantum physics is and what kinds of problems it can solve Know the basic math — from state vectors to quantum matrix manipulations, get the foundation you need to proceed Put quantum physics to work — make sense of Schrödinger's equation and handle particles bound in square wells and harmonic oscillators Solve problems in three dimensions — use the full operators to handle wave functions and eigenvectors to find the natural wave functions of a system Discover the latest research — learn the cutting-edge quantum physics theories that aim to explain the universe itself