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| Author | : Jirí Blank |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 677 |
| Release | : 2008-09-24 |
| Genre | : Science |
| ISBN | : 1402088701 |
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 | : Jirí Blank |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 626 |
| Release | : 1999-04-23 |
| Genre | : Science |
| ISBN | : 9781563961427 |
Market: Mathematicians, researchers, teachers, and graduate students specializing in quantum physics, mathematical physics, and applied mathematics. "I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands quite alone....The translation is remarkably good." John R. Taylor, University of Colorado Based on lectures delivered over the past two decades, this book explains in detail the theory of linear Hilbert-space operators and its uses in quantum physics. The central mathematical tool of this book is the spectral theory of self-adjoint operators, which together with functional analysis and an introduction to the theory of operator sets and algebras, is used in a systematic analysis of the operator aspect of quantum theory. In addition, the theory of Hilbert-space operators is discussed in conjunction with various applications such as Schrodinger operators and scattering theory.
| Author | : Thomas F. Jordan |
| Publisher | : Courier Corporation |
| Total Pages | : 162 |
| Release | : 2012-09-20 |
| Genre | : Science |
| ISBN | : 0486140547 |
Suitable for advanced undergraduates and graduate students, this compact treatment examines linear space, functionals, and operators; diagonalizing operators; operator algebras; and equations of motion. 1969 edition.
| Author | : Werner O. Amrein |
| Publisher | : EPFL Press |
| Total Pages | : 416 |
| Release | : 2009-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781420066814 |
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 | : Philippe Blanchard |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 469 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461200490 |
Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.
| Author | : David W. Cohen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 159 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461388414 |
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 | : Franco Gallone |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 761 |
| Release | : 2014-12-23 |
| Genre | : Science |
| ISBN | : 9814635855 |
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 | : Carlo Alabiso |
| Publisher | : Springer |
| Total Pages | : 267 |
| Release | : 2014-10-08 |
| Genre | : Science |
| ISBN | : 3319037137 |
This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all subjects has been enriched. Moreover, a brief introduction to topological groups has been added in addition to exercises and solved problems throughout the text. With these improvements, the book can be used in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.
| Author | : W.-H. Steeb |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 247 |
| Release | : 2013-03-07 |
| Genre | : Science |
| ISBN | : 9401153329 |
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 | : Robert B. Griffiths |
| Publisher | : Cambridge University Press |
| Total Pages | : 412 |
| Release | : 2003-11-13 |
| Genre | : Science |
| ISBN | : 9780521539296 |
Quantum mechanics is one of the most fundamental yet difficult subjects in physics. Nonrelativistic quantum theory is presented here in a clear and systematic fashion, integrating Born's probabilistic interpretation with Schrödinger dynamics. Basic quantum principles are illustrated with simple examples requiring no mathematics beyond linear algebra and elementary probability theory. The quantum measurement process is consistently analyzed using fundamental quantum principles without referring to measurement. These same principles are used to resolve several of the paradoxes that have long perplexed physicists, including the double slit and Schrödinger's cat. The consistent histories formalism used here was first introduced by the author, and extended by M. Gell-Mann, J. Hartle and R. Omnès. Essential for researchers yet accessible to advanced undergraduate students in physics, chemistry, mathematics, and computer science, this book is supplementary to standard textbooks. It will also be of interest to physicists and philosophers working on the foundations of quantum mechanics.
