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A Primer on Hilbert Space Theory

Carlo Alabiso

Editore: Springer-Verlag Gmbh Okt 2014, 2014
ISBN 10: 3319037129 / ISBN 13: 9783319037127
Nuovi / Buch / Quantità: 1
Da Rhein-Team Lörrach Ivano Narducci e.K. (Lörrach, Germania)
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Titolo: A Primer on Hilbert Space Theory

Casa editrice: Springer-Verlag Gmbh Okt 2014

Data di pubblicazione: 2014

Legatura: Buch

Condizione libro: Neu

Descrizione:

Neuware - 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. 255 pp. Englisch. Codice inventario libreria 9783319037127

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Riassunto:

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.

Dal retro di copertina:

This textbook deals, in a rigorous but reader-friendly fashion, with the geometry of abstract spaces, and in particular with linear, topological, metric and normed spaces, as well as with topological groups. It requires only a basic knowledge of ordinary vector spaces and finite-dimensional matrix calculus, and represents an introduction to more complex arguments, e.g. Hilbert spaces and operators there defined.

The book is based on lectures originally addressed to students in Physics, and the rationale for focusing on only an introduction to the theory of Hilbert space resides in the mathematical complexity of even the simplest physical case of a free particle. From the very beginning, the treatment of this subject requires not only Hilbert space but also distribution theory. Unfortunately, in an ordinary graduate course in Physics there is inadequate time to cover these subjects with sufficient mathematical rigor. Compromises must be found between in-depth studies and practical use of the instruments. In practice, the book builds a pedagogic bridge between the rigorous style of Mathematics and the more practical perspective of Physics.

With respect to the original lectures, all subjects have been slightly enriched, as well as integrated with the study of topological groups. Furthermore, solved problems have been included at the end of each chapter. With these improvements, the book can be used in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.

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Libreria: Rhein-Team Lörrach Ivano Narducci e.K.
Indirizzo: Lörrach, Germania

Libreria AbeBooks dal: 11 gennaio 2012
Valutazione libreria: 5 stelle

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