Quantum Mechanics In Hilbert Space

Author : David W. Cohen
Publisher : Springer Science & Business Media
Page : 159 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461388418

Get Book

An Introduction to Hilbert Space and Quantum Logic by David W. Cohen Pdf

Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and abstract mathematics influence each other we hop back and forth between a purely mathematical development of Hilbert space, and a physically motivated definition of a logic, partially linking the two throughout, and then bringing them together at the deepest level in the last two chapters. This book should be accessible to undergraduate and beginning graduate students in both mathematics and physics. The only strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed.

Author : Michael A. Nielsen,Isaac L. Chuang
Publisher : Cambridge University Press
Page : 709 pages
File Size : 47,9 Mb
Release : 2010-12-09
Category : Science
ISBN : 9781139495486

Get Book

Quantum Computation and Quantum Information by Michael A. Nielsen,Isaac L. Chuang Pdf

One of the most cited books in physics of all time, Quantum Computation and Quantum Information remains the best textbook in this exciting field of science. This 10th anniversary edition includes an introduction from the authors setting the work in context. This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error-correction. Quantum mechanics and computer science are introduced before moving on to describe what a quantum computer is, how it can be used to solve problems faster than 'classical' computers and its real-world implementation. It concludes with an in-depth treatment of quantum information. Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering.

Author : Jirí Blank,Pavel Exner,Miloslav Havlícek
Publisher : Springer Science & Business Media
Page : 677 pages
File Size : 51,9 Mb
Release : 2008-09-24
Category : Science
ISBN : 9781402088704

Get Book

Hilbert Space Operators in Quantum Physics by Jirí Blank,Pavel Exner,Miloslav Havlícek Pdf

The new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.

Author : W.-H. Steeb
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 48,5 Mb
Release : 2013-03-07
Category : Science
ISBN : 9789401153324

Get Book

Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics by W.-H. Steeb Pdf

This book gives a comprehensive introduction to modern quantum mechanics, emphasising the underlying Hilbert space theory and generalised function theory. All the major modern techniques and approaches used in quantum mechanics are introduced, such as Berry phase, coherent and squeezed states, quantum computing, solitons and quantum mechanics. Audience: The book is suitable for graduate students in physics and mathematics.

Author : Eduard Prugovecki
Publisher : Courier Corporation
Page : 722 pages
File Size : 46,5 Mb
Release : 2013-07-02
Category : Science
ISBN : 9780486318059

Get Book

Quantum Mechanics in Hilbert Space by Eduard Prugovecki Pdf

A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas. This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the gap between strictly physics- and mathematics-oriented texts on Hilbert space theory as applied to nonrelativistic quantum mechanics. Organized in the form of definitions, theorems, and proofs of theorems, it allows readers to immediately grasp the basic concepts and results. Exercises appear throughout the text, with hints and solutions at the end.

Author : Werner O. Amrein
Publisher : EPFL Press
Page : 416 pages
File Size : 53,8 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 1420066811

Get Book

Hilbert Space Methods in Quantum Mechanics by Werner O. Amrein Pdf

The necessary foundation in quantum mechanics is covered in this book. Topics include basic properties of Hibert spaces, scattering theory, and a number of applications such as the S-matrix, time delay, and the Flux-Across-Surfaces Theorem.

Author : Anonim
Publisher : Academic Press
Page : 647 pages
File Size : 55,8 Mb
Release : 2003-02-13
Category : Mathematics
ISBN : 9780080873541

Get Book

Quantum Mechanics in Hilbert Space by Anonim Pdf

Quantum Mechanics in Hilbert Space

Author : Eduard Prugovečki
Publisher : Academic Press
Page : 670 pages
File Size : 42,8 Mb
Release : 1971
Category : Mathematics
ISBN : 9780125660501

Get Book

Quantum Mechanics in Hilbert Space by Eduard Prugovečki Pdf

Author : Eduard Prugověcki
Publisher : Unknown
Page : 685 pages
File Size : 44,6 Mb
Release : 1984
Category : Electronic
ISBN : OCLC:797328601

Get Book

Quantum Mechanics in Hilbert Space by Eduard Prugověcki Pdf

Author : Arno Böhm
Publisher : Springer
Page : 96 pages
File Size : 50,9 Mb
Release : 1978
Category : Science
ISBN : UCAL:B3753988

Get Book

The Rigged Hilbert Space and Quantum Mechanics by Arno Böhm Pdf

Author : Franco Gallone
Publisher : World Scientific Publishing Company
Page : 760 pages
File Size : 43,5 Mb
Release : 2014-12-23
Category : Science
ISBN : 9789814635851

Get Book

Hilbert Space and Quantum Mechanics by Franco Gallone Pdf

The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Preface. The book is of interest to researchers and graduate students in functional analysis, who can see how closely an important part of their chosen field is linked with quantum mechanics, and also to physicists, who can see how the abstract language of functional analysis brings unity to the apparently distinct approaches employed in quantum theory.

Author : Guido Fano,S M Blinder
Publisher : Springer
Page : 271 pages
File Size : 44,7 Mb
Release : 2017-06-27
Category : Science
ISBN : 9783319587325

Get Book

Twenty-First Century Quantum Mechanics: Hilbert Space to Quantum Computers by Guido Fano,S M Blinder Pdf

This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result. This book will be of interest to a wide readership seeking to understand modern quantum mechanics and its potential applications.

Author : G. Ludwig
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642700293

Get Book

An Axiomatic Basis for Quantum Mechanics by G. Ludwig Pdf

This book is the first volume of a two-volume work, which is an improved version of a preprint [47] published in German. We seek to deduce the funda mental concepts of quantum mechanics solely from a description of macroscopic devices. The microscopic systems such as electrons, atoms, etc. must be detected on the basis of the macroscopic behavior of the devices. This detection resembles the detection of the dinosaurs on the basis offossils. In this first volume we develop a general description of macroscopic systems by trajectories in state spaces. This general description is a basis for the special de scription of devices consisting of two parts, where the first part is acting on the second. The microsystems are discovered as systems transmitting the action. Axioms which describe general empirical structures of the interactions between the two parts of each device, give rise to a derivation of the Hilbert space structure of quantum mechanics. Possibly, these axioms (and consequently the Hilbert space structure) may fail to describe other realms than the structure of atoms and mole cules, for instance the "elementary particles". This book supplements ref. [2]. Both together not only give an extensive foundation of quantum mechanics but also a solution in principle of the measuring problem.

Author : R. I. G. Hughes
Publisher : Harvard University Press
Page : 388 pages
File Size : 43,9 Mb
Release : 1989
Category : Philosophy
ISBN : 0674843924

Get Book

The Structure and Interpretation of Quantum Mechanics by R. I. G. Hughes Pdf

This important work provides an account of the philosophical foundations of quantum theory that should become a classic text for scientists and nonscientists alike. Hughes offers the first detailed and accessible analysis of the Hilbert-space models used in quantum theory and explains why they are so successful. He goes on to show how the very suitability of Hilbert spaces for modeling the quantum world gives rise to deep problems of interpretation, and makes suggestions about how they can be overcome.

Author : Gerald Teschl
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 40,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821846605

Get Book

Mathematical Methods in Quantum Mechanics by Gerald Teschl Pdf

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).