The Rigged Hilbert Space and Quantum Mechanics
Author | : Arno Böhm |
Publisher | : Springer |
Total Pages | : 96 |
Release | : 1978 |
Genre | : Science |
ISBN | : |
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Author | : Arno Böhm |
Publisher | : Springer |
Total Pages | : 96 |
Release | : 1978 |
Genre | : Science |
ISBN | : |
Author | : A. Böhm |
Publisher | : |
Total Pages | : 69 |
Release | : 1978 |
Genre | : Hilbert space |
ISBN | : |
Author | : A. Böhm |
Publisher | : |
Total Pages | : 69 |
Release | : 1978 |
Genre | : |
ISBN | : |
Author | : A. Böhm |
Publisher | : |
Total Pages | : 0 |
Release | : 1978 |
Genre | : |
ISBN | : |
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 | : Heinz-Dietrich Doebner |
Publisher | : Springer |
Total Pages | : 416 |
Release | : 1998-05-05 |
Genre | : Computers |
ISBN | : |
A Selection of Articles Presented at the 21st International Colloquium on Group Theoretical Methods in Physics (ICGTMP) at Goslar, Germany, July 16-21, 1996
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 | : Carlo Alabiso |
Publisher | : Springer Nature |
Total Pages | : 343 |
Release | : 2021-03-03 |
Genre | : Science |
ISBN | : 3030674177 |
This book offers an essential 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 providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors’s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.
Author | : Arno Böhm |
Publisher | : |
Total Pages | : 151 |
Release | : 1969 |
Genre | : Algebra, Boolean |
ISBN | : 9780387519166 |
Author | : Arno Bohm |
Publisher | : Springer |
Total Pages | : 120 |
Release | : 2014-03-12 |
Genre | : Science |
ISBN | : 9783662137505 |
Dirac's formalism of quantum mechanics was always praised for its elegance. This book introduces the student to its mathematical foundations and demonstrates its ease of applicability to problems in quantum physics. The book starts by describing in detail the concept of Gel'fand triplets and how one can make use of them to make the Dirac heuristic approach rigorous. The results are then deepened by giving the analytic tools, such as the Hardy class function and Hilbert and Mellin transforms, needed in applications to physical problems. Next, the RHS model for decaying states based on the concept of Gamow vectors is presented. Applications are given to physical theories of such phenomena as decaying states and resonances.